{"id":5821,"date":"2026-07-17T11:04:51","date_gmt":"2026-07-17T02:04:51","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=5821"},"modified":"2026-07-17T10:27:26","modified_gmt":"2026-07-17T01:27:26","slug":"9-1_quad","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/9-1_quad\/","title":{"rendered":"9.1 \u6570\u5024\u7a4d\u5206\u306e\u57fa\u672c\u89e3\u6cd5"},"content":{"rendered":"\n<h3>9.1.1 \u57fa\u672c\u7684\u306a\u7a4d\u5206\u516c\u5f0f<\/h3>\n<p>\u7a4d\u5206\u533a\u9593 [a, b] \u3092 n \u5206\u5272\u3059\u308b\u5206\u70b9\u5217\u3092 \\(a = x_0 < x_1 < \\dots < x_n = b\\), \u5404\u5206\u70b9\u306b\u304a\u3051\u308b\u91cd\u307f\u3092 \\(w_i\\), \u5206\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u5024\u3092 \\(f(x_i)\\) \u3068\u3057\u305f\u3068\u304d\u306b, \u7a4d\u5206\u516c\u5f0f\u306e\u4e00\u822c\u7cfb\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b.\n\\[\nI = \\int_a^b f(x) dx \\space \\simeq \\space I_n = \\sum_{i=0}^n w_i f(x_i)\n\\]\n\u5206\u70b9\u304c\u7a4d\u5206\u533a\u9593\u306e\u7aef\u70b9\u306b\u4e00\u81f4\u3057\u306a\u3044\u516c\u5f0f\u3082\u3042\u308a, N \u500b\u306e\u5206\u70b9 a < x_1 < x_2 < \\dots < x_N < b \u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b.\n\\[\n I = \\int_a^b f(x) dx \\space \\simeq I_N = \\sum_{i=1}^N w_i f(x_i)\n\\]\n\u7a4d\u5206\u516c\u5f0f\u306f\u91cd\u307f\u3068\u5206\u70b9\u306e\u3068\u308a\u65b9\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u7a2e\u3005\u306e\u516c\u5f0f\u304c\u5c0e\u304b\u308c\u308b.<\/p>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<th>\u516c\u5f0f<\/th>\n<th>n \u307e\u305f\u306f N<\/th>\n<th>\u91cd\u307f \\(w_i\\)<\/th>\n<th>\u5206\u70b9 \\(x_i\\)<\/th>\n<th>\u53c2\u8003<\/th>\n<\/tr>\n<tr>\n<td>\u53f0\u5f62\u5247<\/td>\n<td>n = 1<\/td>\n<td>\\(w_0 = w_1 = \\frac{b &#8211; a}{2}\\)<\/td>\n<td rowspan=\"3\">\\(h = \\frac{b &#8211; a}{n}\\) (\u7b49\u9593\u9694)<\/td>\n<td>\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u3067 n = 1 \u3068\u3057\u305f\u5834\u5408\u306b\u4e00\u81f4.<\/td>\n<\/tr>\n<tr>\n<td>\u30b7\u30f3\u30d7\u30bd\u30f3\u5247<\/td>\n<td>n = 2<\/td>\n<td>\\(w_0 = w_2 = \\frac{h}{3}, \\space w_1 = 4 \\frac{h}{3}\\)<\/td>\n<td>\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u3067 n = 2 \u3068\u3057\u305f\u5834\u5408\u306b\u4e00\u81f4.<\/td>\n<\/tr>\n<tr>\n<td>\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f<\/td>\n<td>n = 1 \uff5e 7, 9<\/td>\n<td>\u6709\u7406\u6570(\u5206\u6570)\u3067\u8868\u3055\u308c\u308b.<br \/>\nn = 8 \u304a\u3088\u3073 n \\(\\ge\\) 10 \u3067\u306f\u8ca0\u306e\u5024\u304c\u73fe\u308c\u6841\u843d\u3061\u306e\u539f\u56e0\u306b\u306a\u308b\u306e\u3067\u4f7f\u308f\u306a\u3044\u307b\u3046\u304c\u3088\u3044\u3068\u3055\u308c\u3066\u3044\u308b<\/td>\n<td>n \u304c\u5947\u6570\u306e\u3068\u304d\u306f n \u6b21, n \u304c\u5076\u6570\u306e\u3068\u304d\u306f n+1 \u6b21\u307e\u3067\u306e\u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u6b63\u78ba\u306a\u7a4d\u5206\u5024\u3092\u4e0e\u3048\u308b<br \/>\nn = 3 \u306e\u5834\u5408\u3092\u30b7\u30f3\u30d7\u30bd\u30f3\u306e 3\/8 \u5247\u3068\u3088\u3076<\/td>\n<\/tr>\n<tr>\n<td>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f<\/td>\n<td>N = 2 \uff5e 7, 9<\/td>\n<td>\u4e00\u5b9a<\/td>\n<td>\\(a &lt; x_1 &lt; \\dots &lt; x_N &lt; b\\)<br \/>\n(\u4e0d\u7b49\u9593\u9694)<\/td>\n<td>N = 8 \u304a\u3088\u3073 N \\(\\ge\\) 10 \u3067\u306f\u5206\u70b9\u306e\u5024\u304c\u8907\u7d20\u6570\u306b\u306a\u308b\u305f\u3081\u901a\u5e38\u306f\u4f7f\u308f\u308c\u306a\u3044<\/td>\n<\/tr>\n<tr>\n<td>\u30ac\u30a6\u30b9\u578b\u516c\u5f0f<\/td>\n<td>N = 2 \uff5e<\/td>\n<td colspan=\"2\">\u3067\u304d\u308b\u3060\u3051\u7cbe\u5ea6\u304c\u9ad8\u304f\u306a\u308b\u3088\u3046\u306b\u5206\u70b9\u3068\u91cd\u307f\u306e\u4e21\u65b9\u3092\u9078\u3076\u305f\u3081, \u91cd\u307f\u306f\u4e00\u5b9a\u3067\u306f\u306a\u304f\u5206\u70b9\u306f\u4e0d\u7b49\u9593\u9694 \\((a &lt; x_1 &lt; \\dots &lt; x_N &lt; b)\\)<br \/>\n\u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f(\u30ac\u30a6\u30b9\u516c\u5f0f), \u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f, \u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f\u306a\u3069\u306e\u7a2e\u985e\u304c\u3042\u308b<\/td>\n<td>2N &#8211; 1 \u6b21\u307e\u3067\u306e\u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u6b63\u78ba\u306a\u7a4d\u5206\u5024\u3092\u4e0e\u3048\u308b<\/td>\n<\/tr>\n<tr>\n<td>\u30af\u30ec\u30f3\u30b7\u30e7\u30a6\u30fb\u30ab\u30fc\u30c1\u30b9\u516c\u5f0f<\/td>\n<td>n = 2 \uff5e<\/td>\n<td>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u7d1a\u6570\u5c55\u958b\u3088\u308a\u5b9a\u3081\u308b.<\/td>\n<td>\\(x_i = \\frac{b &#8211; a}{2}cos(\\frac{\\pi i}{n}) + \\frac{a + b}{2}\\) \\((i = 0 \\sim n)\\)<\/td>\n<td>\u7279\u7570\u6027\u306e\u5f37\u3044\u95a2\u6570\u3078\u306e\u9069\u7528\u53ef\u80fd\u6027\u304c\u7279\u9577<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<p>\u4ee5\u4e0a\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b, \u7a4d\u5206\u516c\u5f0f\u306f\u5927\u304d\u304f 3 \u3064\u306b\u5206\u3051\u3089\u308c\u308b.<\/p>\n<p>(1) \u5206\u70b9\u304c\u7b49\u9593\u9694\u306e\u3082\u306e: \u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f (\u53f0\u5f62\u5247, \u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u3092\u542b\u3080)<br \/>\n(2) \u91cd\u307f\u304c\u4e00\u5b9a\u306e\u3082\u306e: \u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f<br \/>\n(3) \u5206\u70b9\u9593\u9694\u3082\u91cd\u307f\u3082\u4e00\u5b9a\u3067\u306a\u3044\u3082\u306e: \u30ac\u30a6\u30b9\u578b\u516c\u5f0f, \u30af\u30ec\u30f3\u30b7\u30e7\u30a6\u30fb\u30ab\u30fc\u30c1\u30b9\u516c\u5f0f<\/p>\n<p>\u3044\u305a\u308c\u3082, \u5206\u70b9 \\(x_i\\) \u306b\u304a\u3044\u3066\u95a2\u6570\u5024 \\(f(x_i)\\) \u3092\u3068\u308b\u88dc\u9593\u591a\u9805\u5f0f\u3092\u5b9a\u3081, \u305d\u306e\u7a4d\u5206\u5024\u3092\u6c42\u3081\u308b\u3082\u306e\u3067\u3042\u308b. \u3053\u308c\u3089\u306f<strong>\u88dc\u9593\u578b\u7a4d\u5206\u516c\u5f0f<\/strong>\u3068\u3088\u3070\u308c\u308b.<\/p>\n<h4>9.1.1.1 \u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f<\/h4>\n<p>\u533a\u9593 [a, b] \u3092 n \u7b49\u5206\u3057\u3066\u5206\u70b9\u3092\u7b49\u9593\u9694\u306b\u3068\u308b\u65b9\u6cd5\u3067\u3042\u308b. n = 1 \u306e\u5834\u5408\u306f\u53f0\u5f62\u5247, n = 2 \u306e\u5834\u5408\u306f\u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u3068\u3088\u3070\u308c\u308b.<\/p>\n<p>\u5206\u70b9\u306f \\(a = x_0, x_1, \\dots, x_n = b\\) \u3067\u9593\u9694 \\(h = (b &#8211; a)\/n\\) \u3067\u3042\u308b. \u3059\u306a\u308f\u3061, \\(x_k = a + kh\\) \u3068\u306a\u308b.<\/p>\n<p>\u88ab\u7a4d\u5206\u95a2\u6570 \\(f(x)\\) \u3092\u8fd1\u4f3c\u3059\u308b\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u591a\u9805\u5f0f<sup>(*)<\/sup> \\(p_{n+1}(x)\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b.<br \/>\n\\[<br \/>\np{n+1}(x) = \\sum_{k=0}^n L_k^{(n)}(x) f(x_k)<br \/>\n\\]\n(*) \u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u591a\u9805\u5f0f\u306b\u3064\u3044\u3066\u306f\u300c6. \u88dc\u9593\u6cd5\u300d\u3092\u53c2\u7167\u305b\u3088.<\/p>\n<p>\u3053\u308c\u3092\u7a4d\u5206\u3059\u308b\u3068,<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nI_n &#038; = \\int_a^b p_{n+1}(x) dx \\\\<br \/>\n&#038; = \\sum_{k=0}^n (\\int_a^b L_k^{(n)}(x) dx) f(x_k) \\\\<br \/>\n&#038; = \\frac{b &#8211; a}{n} \\sum_{k=0}^n w_k f(x_k) \\\\<br \/>\n&#038; \u305f\u3060\u3057, w_k = \\frac{n}{b &#8211; a} \\int_a^b L_k^{(n)}(x) dx \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3068\u7a4d\u5206\u516c\u5f0f\u306e\u5f62\u306b\u306a\u308b. \u3053\u308c\u3092 n \u6b21\u306e\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u3068\u3044\u3046. \u3053\u306e\u516c\u5f0f\u306f n \u6b21\u307e\u3067\u306e\u591a\u9805\u5f0f\u306b\u5bfe\u3057\u3066\u6b63\u78ba\u306a\u5024\u3092\u4e0e\u3048\u308b.<\/p>\n<p>\u91cd\u307f \\(w_k\\) \u306f\u591a\u9805\u5f0f\u306e\u8a08\u7b97\u306b\u3088\u308a\u6709\u7406\u6570 (\u5206\u6570) \u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>n = 1 \uff5e 10 \u306e\u3068\u304d\u306e\u91cd\u307f\u306e\u5024\u3092\u300c9.1.4 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868\u300d\u306b\u63b2\u8f09\u3057\u305f. \u8868\u306e\u3088\u3046\u306b n = 8 \u304a\u3088\u3073 n = 10 (\u5b9f\u969b\u306b\u306f n \\(\\ge\\) 10) \u3067\u306f\u8ca0\u306e\u5024\u304c\u73fe\u308c\u308b. \u3053\u308c\u306f\u6841\u843d\u3061\u306e\u539f\u56e0\u306b\u306a\u308b\u306e\u3067 n = 8 \u304a\u3088\u3073 n \\(\\ge\\) 10 \u306e\u516c\u5f0f\u306f\u4f7f\u308f\u306a\u3044\u307b\u3046\u304c\u3088\u3044\u3068\u3055\u308c\u3066\u3044\u308b.<\/p>\n<p>\u4e00\u822c\u7684\u306b\u306f, n \u3092\u5927\u304d\u304f\u3057\u3066\u7cbe\u5ea6\u3092\u4e0a\u3052\u308b\u306e\u3067\u306f\u306a\u304f, \u7a4d\u5206\u533a\u9593\u3092\u5c0f\u533a\u9593\u306b\u5206\u5272\u3057\u3066\u305d\u308c\u305e\u308c\u306b\u516c\u5f0f\u3092\u9069\u7528\u3059\u308b\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u8907\u5408\u516c\u5f0f\u304c\u4f7f\u7528\u3055\u308c\u308b. \u4f8b\u3048\u3070, n = 2 (\u30b7\u30f3\u30d7\u30bd\u30f3\u5247) \u306e\u5834\u5408, [a, b] \u3092 m \u500b\u306e\u5c0f\u533a\u9593\u306b\u5206\u5272\u3057, \u5404\u5c0f\u533a\u9593\u3067\u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u3092\u9069\u7528\u3059\u308b\u3068\u6b21\u306e\u8a08\u7b97\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; I_{2m} = \\frac{h}{3}(f(x_0) + 2 \\sum_{j=1}^{m-1} f(x_{2j}) + 4 \\sum_{j=1}^m f(x_{2j-1}) + f(x_{2m})) \\\\<br \/>\n&#038; \u305f\u3060\u3057, \\space h = \\frac{b &#8211; a}{2m}, \\space x_j = a + jh \\space (j = 0, 1, \\dots, 2m) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u308c\u306f\u8907\u5408\u30b7\u30f3\u30d7\u30bd\u30f3\u516c\u5f0f\u3068\u3088\u3070\u308c\u308b.<\/p>\n<h4>9.1.1.2 \u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f<\/h4>\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u3068\u306f\u9006\u306b\u91cd\u307f\u304c\u4e00\u5b9a\u306b\u306a\u308b\u3088\u3046\u306b\u5206\u70b9\u3092\u9078\u3076\u65b9\u6cd5\u3067\u3042\u308b.<\/p>\n<p>\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b.<br \/>\n\\[<br \/>\nI_N = \\frac{b &#8211; a}{N} \\sum_{k=1}^N f(\\frac{a + b}{2} + \\frac{(b &#8211; a)}{2}x_k)<br \/>\n\\]\n\\(x_k\\) \u306f\u5206\u70b9\u3067, \u591a\u9805\u5f0f \\(p_N(x) = \\prod_{k=1}^N (x &#8211; x_k) = \\sum_{i=0}^N a_i x^{N-i}\\) \u3092\u30bc\u30ed\u3068\u304a\u3044\u305f\u65b9\u7a0b\u5f0f\u306e N \u500b\u306e\u89e3\u3068\u3057\u3066\u6c42\u3081\u3089\u308c\u308b. \u5c55\u958b\u3057\u305f\u591a\u9805\u5f0f\u306e\u4fc2\u6570 \\(a_i\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b (\u5c0e\u51fa\u306e\u8a73\u7d30\u306f\u6587\u732e[3]\u3092\u53c2\u7167).<br \/>\n\\[<br \/>\na_0 = 1 \\\\<br \/>\n\\begin{equation}<br \/>\na_i =<br \/>\n\\begin{cases}<br \/>\n-\\frac{N}{i} \\sum_{j=2,4,\\dots}^{i} \\frac{a_{i-j}}{j + 1} &#038; (i = 2, 4, \\dots, N2) \\\\<br \/>\n0 &#038; (i = 1, 3, \\dots, N1) \\\\<br \/>\n\\end{cases}<br \/>\n\\end{equation}<br \/>\n\\]\n\u305f\u3060\u3057, N1 = N &#8211; 1, N2 = N (N \u304c\u5076\u6570\u306e\u3068\u304d), N1 = N, N2 = N &#8211; 1 (N \u304c\u5947\u6570\u306e\u3068\u304d).<\/p>\n<p>N = 2 \uff5e 7, 9 \u306e\u3068\u304d\u306e\u5206\u70b9\u306e\u5024\u3092\u300c9.1.4 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868\u300d\u306b\u63b2\u8f09\u3057\u305f. N = 8 \u3068 N \\(\\ge\\) 10 \u306f\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u8907\u7d20\u6570\u304c\u542b\u307e\u308c, \u8a08\u7b97\u304c\u8907\u96d1\u306b\u306a\u308b\u3046\u3048\u7cbe\u5ea6\u306e\u70b9\u3067\u3082\u4e0d\u5229\u306a\u305f\u3081\u901a\u5e38\u306f\u4f7f\u7528\u3055\u308c\u306a\u3044.<\/p>\n<h4>9.1.1.3 \u30ac\u30a6\u30b9\u578b\u516c\u5f0f<\/h4>\n<p>\u3067\u304d\u308b\u3060\u3051\u7cbe\u5ea6\u304c\u9ad8\u304f\u306a\u308b\u3088\u3046\u306b\u5206\u70b9\u3068\u91cd\u307f\u306e\u4e21\u65b9\u3092\u9078\u3076\u65b9\u6cd5\u3067\u3042\u308b. \u88ab\u7a4d\u5206\u95a2\u6570\u3092\u76f4\u4ea4\u591a\u9805\u5f0f\u88dc\u9593<sup>(*)<\/sup>\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u6c42\u3081\u3089\u308c, 2N &#8211; 1 \u6b21\u307e\u3067\u306e\u591a\u9805\u5f0f\u306b\u5bfe\u3057\u3066\u6b63\u78ba\u306a\u5024\u3092\u4e0e\u3048\u308b.<\/p>\n<p>(*) \u76f4\u4ea4\u591a\u9805\u5f0f\u304a\u3088\u3073\u76f4\u4ea4\u591a\u9805\u5f0f\u88dc\u9593\u306b\u3064\u3044\u3066\u306f\u300c6. \u88dc\u9593\u6cd5\u300d\u3092\u53c2\u7167\u305b\u3088.<\/p>\n<p>\u533a\u9593 [a, b] \u306b\u304a\u3051\u308b f(x)w(x) \u306e\u7a4d\u5206\u3092\u8003\u3048\u308b. w(x) \u306f\u5bc6\u5ea6\u95a2\u6570\u3067\u3042\u308b.<br \/>\n\\[<br \/>\nI = \\int_a^b f(x) w(x) dx<br \/>\n\\]\nf(x) \u3092\u76f4\u4ea4\u591a\u9805\u5f0f\u88dc\u9593\u95a2\u6570 \\(f_N(x)\\) \u3067\u7f6e\u304d\u63db\u3048\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nI_N &#038; = \\int_a^b f_N(x)w(x) dx \\\\<br \/>\n&#038; = \\sum_{j=0}^{N-1} \\frac{1}{\\lambda_j} \\sum_{k=1}^N w_k p_j(x_k) f(x_k) \\int_a^b p_j(x) w(x) dx \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\\(p_j(x)\\) \u306e\u76f4\u4ea4\u6027\u3088\u308a\u4e0a\u5f0f\u306e\u7a4d\u5206\u306e\u90e8\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u7c21\u5358\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{equation}<br \/>\n\\int_a^b p_j(x) w(x) dx =<br \/>\n\\begin{cases}<br \/>\n\\frac{\\lambda_0}{\\mu_0} &#038; (j = 0) \\\\<br \/>\n0 &#038; (j \\ne 0) \\\\<br \/>\n\\end{cases}<br \/>\n\\end{equation}<br \/>\n\\]\n\u3059\u306a\u308f\u3061, \\(I_N\\) \u306e\u5f0f\u306b\u304a\u3044\u3066\u5916\u5074\u306e \\(\\sigma\\) \u306f \\(j = 0\\) \u4ee5\u5916\u306e\u9805\u306f \\(0\\) \u306b\u306a\u308a, \u307e\u305f \\(p_0(x) = \\mu_0\\) \u3067\u3042\u308b\u304b\u3089, \u6b21\u306e\u30ac\u30a6\u30b9\u578b\u7a4d\u5206\u516c\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nI_N &#038; = \\frac{1}{\\lambda_0} \\frac{\\lambda_0}{\\mu_0} \\sum_{k=1}^N w_k p_0(x_k) f(x_k) \\\\<br \/>\n&#038; = \\sum_{k=1}^N w_k f(x_k) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u3053\u3067, \u5206\u70b9 \\(x_k\\) \u306f\u76f4\u4ea4\u591a\u9805\u5f0f\u306e\u30bc\u30ed\u70b9\u3067\u3042\u308b. \u91cd\u307f \\(w_k\\) \u306f\u76f4\u4ea4\u591a\u9805\u5f0f\u88dc\u9593\u306e \\(w_k\\) \u306b\u7b49\u3057\u304f, \u6b21\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b.<br \/>\n\\[<br \/>\nw_k = \\frac{\\mu_N \\lambda_{N-1}}{\\mu_{N-1} p_{N-1}(x_k) p&#8217;_N(x_k)}<br \/>\n\\]\n\u76f4\u4ea4\u591a\u9805\u5f0f\u306e\u7a2e\u985e\u306b\u5fdc\u3058\u3066\u3044\u304f\u3064\u304b\u306e\u7a4d\u5206\u516c\u5f0f\u304c\u3042\u308a, \u4ee3\u8868\u7684\u306a\u3082\u306e\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<br \/>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<th>\u76f4\u4ea4\u591a\u9805\u5f0f<\/th>\n<th>\u7a4d\u5206\u516c\u5f0f<\/th>\n<th>\u533a\u9593 [a, b]<\/th>\n<th>\u5bc6\u5ea6\u95a2\u6570 w(x)<\/th>\n<\/tr>\n<tr>\n<td>\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f \\(P_n(x)\\)<\/td>\n<td>\u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f (\u30ac\u30a6\u30b9\u516c\u5f0f)<\/td>\n<td>[-1, 1]<\/td>\n<td>1<\/td>\n<\/tr>\n<td>\u30e9\u30b2\u30fc\u30eb\u591a\u9805\u5f0f \\(L_n(x)\\)<\/td>\n<td>\u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f<\/td>\n<td>[0, \\(+\\infty\\)]<\/td>\n<td>\\(e^{-x}\\)<\/td>\n<\/tr>\n<td>\u30a8\u30eb\u30df\u30fc\u30c8\u591a\u9805\u5f0f \\(H_n(x)\\)<\/td>\n<td>\u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f<\/td>\n<td>[\\(-\\infty\\), \\(+\\infty\\)]<\/td>\n<td>\\(e^{-x^2}\\)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n<h4>(1) \u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f (\u30ac\u30a6\u30b9\u516c\u5f0f)<\/h4>\n<p>\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3057\u3066, \\(p_n(x) = P_n(x), w(x) = 1, [a, b] = [-1, 1]\\) \u3068\u3059\u308b\u3068\u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f\u304c\u5f97\u3089\u308c\u308b. \u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f\u306f\u5358\u306b\u30ac\u30a6\u30b9\u516c\u5f0f\u3068\u3088\u3070\u308c\u308b\u3053\u3068\u304c\u591a\u3044.<br \/>\n\\[<br \/>\nI = \\int_{-1}^{1} f(x) dx \\simeq I_N = \\sum_{k=1}^N w_k f(x_k)<br \/>\n\\]\n\u305f\u3060\u3057, \\(x_k\\) \u306f \\(P_n(x) = 0\\) \u306e N \u500b\u306e\u30bc\u30ed\u70b9\u3067\u3042\u308b. \\(w_k\\) \u306f, \\(\\lambda_N = 2\/(2N + 1)\\), \\(\\mu_N = \\prod_{k=1}^N (2k \u2013 1)\/k\\) \u304b\u3089, \u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nw_k &#038; = \\frac{2}{nP_{N-1}(x_k)P&#8217;_N(x_k)} \\\\<br \/>\n&#038; = \\frac{2(1 &#8211; x_k^2)}{(nP_{N-1}(x_k))^2} \\\\<br \/>\n\\end{align}<br \/>\n\\]\nN = 2 \uff5e 10 \u306e\u3068\u304d\u306e\u5206\u70b9\u304a\u3088\u3073\u91cd\u307f\u306e\u5024\u3092\u300c9.1.4 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868\u300d\u306b\u63b2\u8f09\u3057\u305f.<\/p>\n<p>\u4efb\u610f\u306e\u533a\u9593 [a, b] \u306e\u7a4d\u5206\u3092\u6c42\u3081\u308b\u3068\u304d\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u3088\u3044.<br \/>\n\\[<br \/>\nI = \\int_a^b f(x) dx \\simeq I_N = \\frac{b &#8211; a}{2} \\sum_{k=1}^N w_k f(\\frac{a + b}{2} + \\frac{b &#8211; a}{2}x_k)<br \/>\n\\]\n<h4>(2) \u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f<\/h4>\n<p>\u30e9\u30b2\u30fc\u30eb\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3057\u3066, \\(p_n(x) = L_n(x), w(x) = e^{-x}, [a, b] = [0, +\\infty]\\) \u3068\u3059\u308b\u3068\u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\nI = \\int_0^{\\infty} e^{-x} f(x) dx \\simeq I_N = \\sum_{k=1}^N w_k f(x_k)<br \/>\n\\]\n\u305f\u3060\u3057, \\(x_k\\) \u306f \\(L_n(x) = 0\\) \u306e N \u500b\u306e\u30bc\u30ed\u70b9\u3067\u3042\u308b. \\(w_k\\) \u306f, \\(\\lambda_N = 1, \\mu_N = (-1)^n\/n!\\) \u3088\u308a, \u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<br \/>\n\\[<br \/>\nw_k = -\\frac{1}{NL_{N-1}(x_k)L&#8217;_N(x_k)} = \\frac{x_k}{n^2 L_{N-1}(x_k)^2}<br \/>\n\\]\nN = 2 \uff5e 10 \u306e\u3068\u304d\u306e\u5206\u70b9\u304a\u3088\u3073\u91cd\u307f\u306e\u5024\u3092\u300c9.1.4 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868\u300d\u306b\u63b2\u8f09\u3057\u305f.<\/p>\n<h4>(3) \u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f<\/h4>\n<p>\u30a8\u30eb\u30df\u30fc\u30c8\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3057\u3066, \\(p_n(x) = H_n(x), w(x) = e^{-x^2}, [a, b] = [-\\infty, +\\infty]\\) \u3068\u3059\u308b\u3068\u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\nI = \\int_{-\\infty}^{+\\infty} f(x) e^{-x^2} dx \\simeq I_N = \\sum_{k=1}^N w_k f(x_k)<br \/>\n\\]\n\u305f\u3060\u3057, \\(x_k\\) \u306f \\(H_n(x) = 0\\) \u306e N \u500b\u306e\u30bc\u30ed\u70b9\u3067\u3042\u308b. \\(w_k\\) \u306f, \\(\\lambda_N = \\pi^{1\/2} 2^n n!, \\mu_N = 2^n\\) \u3088\u308a, \u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<br \/>\n\\[<br \/>\nw_k = \\frac{\\pi^{1\/2} 2^n (n &#8211; 1)!}{H_{N-1}(x_k) H&#8217;_N(x_k)} = \\frac{\\pi^{1\/2} 2^{n-1} (n &#8211; 1)!} {nH_{N-1}(x_k)^2}<br \/>\n\\]\nN = 2 \uff5e 10 \u306e\u3068\u304d\u306e\u5206\u70b9\u304a\u3088\u3073\u91cd\u307f\u306e\u5024\u3092\u300c9.1.4 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868\u300d\u306b\u63b2\u8f09\u3057\u305f.<\/p>\n<h4>(4) \u30af\u30ec\u30f3\u30b7\u30e7\u30a6\u30fb\u30ab\u30fc\u30c1\u30b9\u516c\u5f0f<\/h4>\n<h4>(i) \u6ed1\u3089\u304b\u306a\u95a2\u6570\u306e\u7a4d\u5206<\/h4>\n<p>\u88ab\u7a4d\u5206\u95a2\u6570 f(x) \u3092\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u7d1a\u6570\u5c55\u958b\u3057, \u9805\u5225\u306b\u7a4d\u5206\u3059\u308b\u65b9\u6cd5\u3067\u3042\u308b. \u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u7d1a\u6570\u306e\u53ce\u675f\u304c\u901f\u3044\u95a2\u6570\u3067\u3042\u308c\u3070\u5c11\u306a\u3044\u95a2\u6570\u8a08\u7b97\u56de\u6570\u3067\u7a4d\u5206\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>\u533a\u9593 [-1, 1] \u3067\u6ed1\u3089\u304b\u306a\u95a2\u6570 f(x) \u3092\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u7d1a\u6570\u5c55\u958b\u3059\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; f(x) = \\frac{1}{2}a_0 + \\sum_{k=1}^{\\infty} a_k T_k(x) \\\\<br \/>\n&#038; T_k(x) = cos(k\\theta), x = cos(\\theta) \\\\<br \/>\n&#038; a_k = \\frac{2}{\\pi} \\int_0^{\\pi} f(cos(\\theta))cos(k\\theta) d\\theta \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u4fc2\u6570 \\(a_k\\) \u306e\u7a4d\u5206\u3092\u53f0\u5f62\u5247\u3067\u8a08\u7b97\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\na_k^{(n)} = \\frac{1}{n}f(1) + \\frac{2}{n}\\sum_{j=1}^{n-1} f(cos(\\frac{j\\pi}{n})) cos(\\frac{kj\\pi}{n}) + (-1)^k\\frac{1}{n}f(-1)<br \/>\n\\]\n\u53f3\u4e0a\u6dfb\u5b57\u306e (n) \u306f, n \u5c0f\u533a\u9593\u306e\u8907\u5408\u53f0\u5f62\u5247\u3092\u4f7f\u3063\u305f\u3053\u3068\u3092\u793a\u3059. \u3053\u306e\u4fc2\u6570\u306f FFT (\u30b3\u30b5\u30a4\u30f3\u5909\u63db) \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u3063\u3066\u52b9\u7387\u7684\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b (XLPack \u3067\u3042\u308c\u3070 Cost1f \u304c\u4f7f\u3048\u308b).<\/p>\n<p>f(x) \u306e\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u7d1a\u6570\u5c55\u958b\u3092\u7b2c n \u9805\u307e\u3067\u3067\u6253\u3061\u5207\u3063\u3066\u7a4d\u5206\u3092\u6b21\u306e\u3088\u3046\u306b\u8fd1\u4f3c\u3059\u308b.<br \/>\n\\[<br \/>\nI = \\int_a^b f(x) dx \\simeq I_n = \\frac{1}{2}a_0^{(n)} \\int_{-1}^1 T_0(x) dx + \\sum_{k=1}^{n-1} a_k^{(n)} \\int_{-1}^1 T_k(x) dx + \\frac{1}{2}a_n^{(n)} \\int_{-1}^{1} T_n(x) dx<br \/>\n\\]\n\u3053\u306e\u3088\u3046\u306b\u9805\u5225\u306e\u7a4d\u5206\u306e\u5f62\u306b\u306a\u308b. \u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u591a\u9805\u5f0f\u306e\u9805\u306e\u7a4d\u5206\u306f\u6b21\u306e\u95a2\u4fc2\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b (\u7a4d\u5206\u5b9a\u6570\u306f\u7701\u7565\u3057\u3066\u8868\u793a\u3057\u305f).<br \/>\n\\[<br \/>\n\\begin{equation}<br \/>\n\\int T_k dx =<br \/>\n\\begin{cases}<br \/>\nT_1(x) &#038; (k = 0) \\\\<br \/>\n\\frac{1}{4}(T_2(x) + 1) &#038; (k = 1) \\\\<br \/>\n\\frac{1}{2}(\\frac{T_{k+1}(x)}{k + 1} &#8211; \\frac{T_{k-1}(x)}{k &#8211; 1}) &#038; (k \\ge 2) \\\\<br \/>\n\\end{cases}<br \/>\n\\end{equation}<br \/>\n\\]\n\u4ee5\u4e0a\u306e\u95a2\u4fc2\u5f0f\u3092\u4f7f\u3063\u3066 f(x) \u306e [-1, 1] \u306b\u304a\u3051\u308b\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b (\u3053\u306e\u5834\u5408, k \u304c\u5947\u6570\u306e \\(\\int_{-1}^1 T_k dx\\) \u306f 0 \u306b\u306a\u308b).<\/p>\n<p>\u4efb\u610f\u306e\u533a\u9593 [a, b] \u306e\u7a4d\u5206\u3092\u6c42\u3081\u308b\u306b\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u3088\u3044.<br \/>\n\\[<br \/>\nx = \\frac{b &#8211; a}{2} cos(\\theta) + \\frac{a + b}{2}<br \/>\n\\]\n<h4>(ii) \u7279\u7570\u6027\u304c\u5f37\u3044\u95a2\u6570\u306e\u7a4d\u5206<\/h4>\n<p>\u30af\u30ec\u30f3\u30b7\u30e7\u30a6\u30fb\u30ab\u30fc\u30c1\u30b9\u516c\u5f0f\u3067 \\(f(x)w(x)\\) \u306e\u5f62\u306e\u95a2\u6570\u3092\u7a4d\u5206\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u308b. \\(w(x)\\) \u306f\u7279\u7570\u6027\u304c\u5f37\u3044\u3088\u3046\u306a\u95a2\u6570\u3092\u60f3\u5b9a\u3057\u3066, \\(f(x)\\) \u3060\u3051\u3092\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u7d1a\u6570\u5c55\u958b\u3057 \\(w(x)\\) \u3092\u542b\u3080\u9805\u5225\u7a4d\u5206\u306f\u5225\u9014\u884c\u3046\u3053\u3068\u306b\u3059\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nI &#038; = \\int_{-1}^{1} f(x)w(x)dx \\\\<br \/>\n&#038; \\simeq I_n = \\frac{1}{2}a_0^{(n)}\\int_{-1}^{1}T_0(x)w(x)dx + \\sum_{k=1}^{n-1}a_k^{(n)}\\int_{-1}^{1}T_k(x)w(x)dx + \\frac{1}{2}a_n^{(n)}\\int_{-1}^1 T_n(x)w(x)dx \\\\<br \/>\n&#038; = \\frac{1}{2}a_0^{(n)}\\mu_0 + \\sum_{k=1}^{n-1}a_k^{(n)}\\mu_k + \\frac{1}{2}a_n^{(n)}\\mu_n \\\\<br \/>\n&#038; \u305f\u3060\u3057, \\space \\mu_k = \\int_{-1}^{1} T_k(x)w(x) dx \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\\(\\mu_k\\) \u306f\u30e2\u30fc\u30e1\u30f3\u30c8\u3068\u3088\u3070\u308c\u308b. \u30e2\u30fc\u30e1\u30f3\u30c8\u304c\u5b89\u5b9a\u7684\u306b\u8a08\u7b97\u3067\u304d\u308b (\u4f8b\u3048\u3070, \u89e3\u6790\u7684\u306b) \u3088\u3046\u306a \\(w(x)\\) \u3092\u542b\u3080\u7a4d\u5206\u306b\u3064\u3044\u3066\u306f\u7279\u7570\u6027\u304c\u5f37\u304f\u3066\u3082\u30af\u30ec\u30f3\u30b7\u30e7\u30a6\u30fb\u30ab\u30fc\u30c1\u30b9\u516c\u5f0f\u3067\u8a08\u7b97\u3067\u304d\u308b\u3053\u3068\u306b\u306a\u308b.<\/p>\n<p>\u6b21\u306e\u7a4d\u5206\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\nI = \\int_{-1}^{1} \\frac{f(x)}{x &#8211; c} dx<br \/>\n\\]\n\u3053\u308c\u306f\u30b3\u30fc\u30b7\u30fc\u306e\u4e3b\u5024\u7a4d\u5206\u3067\u3042\u308b. <\/p>\n<p>\\(w(x) = 1\/(x &#8211; c)\\) \u306b\u3064\u3044\u3066\u30e2\u30fc\u30e1\u30f3\u30c8\u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u308b (\u6587\u732e[6]\u53c2\u7167).<br \/>\n\\[<br \/>\n\\mu_0 = ln|\\frac{1 &#8211; c}{1 + c}| \\\\<br \/>\n\\mu_1 = 2 + c\\mu_0 \\\\<br \/>\n\\begin{equation}<br \/>\n\\mu_{k+1} &#8211; 2c\\mu_k + \\mu_{k-1} =<br \/>\n\\begin{cases}<br \/>\n0 &#038; (k \u304c\u5947\u6570) \\\\<br \/>\n\\frac{4}{1 &#8211; k^2} &#038; (k \u304c\u5076\u6570) \\\\<br \/>\n\\end{cases}<br \/>\n\\end{equation}<br \/>\n\\]\n\\(c\\) \u306e\u5024\u304c \\([-1-\\epsilon, 1+\\epsilon]\\) (\\(\\epsilon\\) \u306f\u304a\u304a\u3080\u306d 0.1) \u306e\u4e2d\u306b\u3042\u308c\u3070\u4e0a\u5f0f\u306f\u5b89\u5b9a\u306b\u8a08\u7b97\u3067\u304d\u308b. \u305d\u3046\u3067\u306a\u3051\u308c\u3070, \\(c\\) \u306f\u7a4d\u5206\u7bc4\u56f2\u304b\u3089\u5341\u5206\u306b\u9060\u304f\u306b\u3042\u308b\u3068\u307f\u306a\u3057\u3066\u901a\u5e38\u306e\u30ac\u30a6\u30b9\u516c\u5f0f\u306a\u3069\u3067\u8a08\u7b97\u3067\u304d\u308b.<\/p>\n<p>\u6587\u732e[6]\u3067\u306f\u4ed6\u306b\u4ee5\u4e0b\u306e\u95a2\u6570\u306b\u3064\u3044\u3066\u306e\u8a08\u7b97\u6cd5\u3082\u793a\u3055\u308c\u3066\u304a\u308a, \u3053\u308c\u3089\u306e\u8a08\u7b97\u6cd5\u306f QUADPACK \u306e\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u3067\u63a1\u7528\u3055\u308c\u3066\u3044\u308b.<\/p>\n<ul>\n<li>\\(sin(\\omega x)\\) \u304a\u3088\u3073 \\(cos(\\omega x)\\)<\/li>\n<li>\\((x &#8211; a)^{\\alpha} (b &#8211; x)^{\\beta} log^{\\mu}(x &#8211; a) log^{\\nu}(b &#8211; x)\\) (\\(\\mu\\), \\(\\nu\\) = 0 \u307e\u305f\u306f 1)<\/li>\n<\/ul>\n<h3>9.1.2 \u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206<\/h3>\n<p>\u6570\u5217 \\(a_k\\) \u304c\u5b9a\u6570 \\(a\\) \u306b\u53ce\u675f\u3059\u308b\u3082\u306e\u3068\u3057\u3066, \u53ce\u675f\u7387 \\(\\lambda\\)\u3092<br \/>\n\\[<br \/>\n\\lambda = \\lim_{k \\to \\infty} \\frac{a_{k+1} &#8211; a}{a_k &#8211; a}<br \/>\n\\]\n\u3068\u5b9a\u7fa9\u3059\u308b. \\(\\lambda\\) \u306e\u5024\u304c\u4e8b\u524d\u306b\u308f\u304b\u3063\u3066\u3044\u308b\u3068\u3057\u3066, \u3053\u308c\u3092 \\(a\\) \u306b\u3064\u3044\u3066\u89e3\u3044\u3066\u6c42\u3081\u305f\u5024<br \/>\n\\[<br \/>\nb_k = \\frac{a_{k+1} &#8211; \\lambda a_k}{1 &#8211; \\lambda}<br \/>\n\\]\n\u306b\u3088\u308b\u6570\u5217 {\\(b_k\\)} \u306f\u5143\u306e\u6570\u5217 {\\(a_k\\)} \u3088\u308a\u3082\u901f\u304f\u53ce\u675f\u3059\u308b\u3068\u4e88\u60f3\u3055\u308c\u308b. \u3053\u308c\u3092\u30ea\u30c1\u30e3\u30fc\u30c9\u30bd\u30f3\u306e\u52a0\u901f\u6cd5\u3068\u3044\u3046.<\/p>\n<p>\u8907\u5408\u53f0\u5f62\u5247\u306b\u304a\u3044\u3066\u5206\u70b9\u6570\u3092\u500d\u3005\u306b\u3057\u305f\u7cfb\u5217 \\(I_1, I_2, \\dots\\) \u3092\u4f5c\u308c\u3070, h \u306f\u534a\u3005\u306b\u306a\u3063\u3066\u3086\u304d, \u8aa4\u5dee\u306f 1 \u6bb5\u9032\u3080\u3054\u3068\u306b 1\/4 \u306b\u306a\u308b (\u3059\u306a\u308f\u3061\u53ce\u675f\u7387\u304c 1\/4: \u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u306e\u9805\u3092\u53c2\u7167\u305b\u3088). \u3053\u308c\u306b\u30ea\u30c1\u30e3\u30fc\u30c9\u30bd\u30f3\u306e\u52a0\u901f\u6cd5\u3092\u9069\u7528\u3057\u305f\u88dc\u5916\u3092\u884c\u3044,<br \/>\n\\[<br \/>\nI_k^{(1)} = \\frac{I_{k+1} &#8211; \\lambda I_k}{1 &#8211; \\lambda} = \\frac{4 I_{k+1} &#8211; I_k}{4 &#8211; 1}<br \/>\n\\]\n\u3068\u3057\u305f\u7cfb\u5217 { \\(I_1^{(1)}, I_2^{(1)}, \\dots\\) } \u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b. \u3053\u308c\u306f\u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u306b\u4e00\u81f4\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b. \u53ce\u675f\u7387 \\(\\lambda^{(1)}\\) \u306f \\(1\/4^2\\) \u306b\u306a\u308b. \u66f4\u306b\u53ce\u675f\u3092\u52a0\u901f\u3059\u308b\u305f\u3081\u306b\u65b0\u3057\u3044\u7cfb\u5217\u306b\u7b2c 2 \u56de\u88dc\u5916\u3092\u884c\u3046\u3068<br \/>\n\\[<br \/>\nI_k^{(2)} = \\frac{I_{k+1}^{(1)} &#8211; \\lambda^{(1)} I_k^{(1)}}{1 &#8211; \\lambda^{(1)}} = \\frac{4^2 I_{k+1}^{(1)} &#8211; I_k^{(1)}}{4^2 &#8211; 1}<br \/>\n\\]\n\u3068\u3057\u305f\u7cfb\u5217 { \\(I_1^{(2)}, I_2^{(2)}, \\dots\\) } \u3092\u5f97\u308b. \u3053\u306e\u3088\u3046\u306b\u88dc\u5916\u3092\u7e70\u308a\u8fd4\u3057\u3066\u53ce\u675f\u3092\u52a0\u901f\u3059\u308b\u65b9\u6cd5\u3092\u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206\u6cd5\u3068\u3044\u3046.<\/p>\n<p>\u8907\u5408\u53f0\u5f62\u5247\u306b\u304a\u3044\u3066\u5206\u70b9\u6570\u3092\u500d\u3005\u306b\u3057\u3066\u3044\u304f\u969b\u306b\u306f, \u6bce\u56de\u534a\u5206\u306f\u500d\u306b\u3059\u308b\u524d\u306e\u5206\u70b9\u3068\u4e00\u81f4\u3059\u308b\u306e\u3067\u534a\u5206\u3060\u3051\u8a08\u7b97\u3059\u308c\u3070\u3088\u3044\u3053\u3068\u306b\u306a\u308b.<\/p>\n<h3>9.1.3 \u6570\u5024\u5b9f\u9a13<\/h3>\n<p>\u3053\u3053\u307e\u3067\u8aac\u660e\u3057\u305f\u7a4d\u5206\u516c\u5f0f\u306b\u3064\u3044\u3066\u3044\u304f\u3064\u304b\u306e\u4f8b\u984c\u95a2\u6570\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u7cbe\u5ea6\u3092\u6bd4\u8f03\u3059\u308b. \u306a\u304a, \u8a08\u7b97\u306f VBA \u306e Double \u578b\u3092\u4f7f\u3063\u3066 64 \u30d3\u30c3\u30c8\u500d\u7cbe\u5ea6 (10 \u9032 15 \uff5e 16 \u6841) \u3067\u884c\u3063\u305f.<\/p>\n<h3>9.1.3.1 \u6709\u9650\u533a\u9593\u306e\u7a4d\u5206<\/h3>\n<h4>\u6570\u5024\u5b9f\u9a13 (1) \u6027\u8cea\u306e\u826f\u3044\u95a2\u6570<\/h4>\n<p>\u6b21\u306e\u7a4d\u5206\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\nI = \\int_0^1  e^x cos(x) dx = 1.378024613547364<br \/>\n\\]\n\u3053\u308c\u306f\u6027\u8cea\u306e\u826f\u3044 (\u89e3\u6790\u7684\u306a) \u95a2\u6570\u3067, \u30b0\u30e9\u30d5\u306b\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306a\u5f62\u3092\u3057\u3066\u3044\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_1_exp1_F.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5880\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_1_exp1_F.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_1_exp1_F-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u308c\u3092\u7a2e\u3005\u306e\u7a4d\u5206\u516c\u5f0f\u3067\u5206\u70b9\u6570 N (= \u95a2\u6570\u8a55\u4fa1\u56de\u6570) (\u6a2a\u8ef8) \u3092\u5909\u3048\u3066\u8a08\u7b97\u3057, \u305d\u306e\u6642\u306e\u76f8\u5bfe\u8aa4\u5dee (\u7e26\u8ef8) \u3092\u5bfe\u6570\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_1_exp1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5881\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_1_exp1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_1_exp1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u53f0\u5f62\u5247\u306f\u5c0f\u533a\u9593\u6570\u3092 N &#8211; 1 \u3068\u3057\u305f\u8907\u5408\u516c\u5f0f\u306e\u7d50\u679c\u3092\u793a\u3057\u305f. \u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u306f\u5c0f\u533a\u9593\u6570\u3092 (N &#8211; 1)\/2 \u3068\u3057\u305f\u8907\u5408\u516c\u5f0f\u306e\u7d50\u679c\u3092\u793a\u3057\u305f. \u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u304a\u3088\u3073\u30af\u30ec\u30f3\u30b7\u30e7\u30a6\u30fb\u30ab\u30fc\u30c1\u30b9\u516c\u5f0f\u3067\u306f N = n + 1 \u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n<p>\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u304a\u3088\u3073\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f\u3067\u306f\u5206\u70b9\u6570\u304c\u5076\u6570\u3088\u308a\u3082\u5947\u6570\u306e\u307b\u3046\u304c\u6210\u7e3e\u304c\u3088\u3044.<\/p>\n<p>\u30ac\u30a6\u30b9\u516c\u5f0f\u306f\u4ed6\u306b\u6bd4\u3079\u3066\u7cbe\u5ea6\u304c\u3088\u304f, \u53ef\u80fd\u3067\u3042\u308c\u3070\u3053\u306e\u516c\u5f0f\u3092\u4f7f\u3046\u306e\u304c\u3088\u3044. N = 7 \u4ee5\u4e0a\u3067\u982d\u6253\u3061\u306a\u306e\u306f\u500d\u7cbe\u5ea6\u8a08\u7b97\u306e\u4e38\u3081\u8aa4\u5dee\u306e\u305f\u3081\u3067\u3042\u308b.<\/p>\n<p>\u5206\u70b9\u3092\u500d\u3005\u306b\u5897\u3084\u3057\u3066\u3044\u3063\u305f\u3068\u304d\u306e\u53f0\u5f62\u5247\u306e\u8a08\u7b97\u7d50\u679c\u306b\u7740\u76ee\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b.<br \/>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<th>\u5206\u70b9\u6570<\/th>\n<th>\u7a4d\u5206\u5024(\u8a08\u7b97\u5024)<\/th>\n<th>\u7a4d\u5206\u5024(\u771f\u5024)<\/th>\n<th>\u8aa4\u5dee<\/th>\n<th>\u53ce\u675f\u7387<\/th>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>1.34061800327106<\/td>\n<td>1.37802461354736<\/td>\n<td>0.037406610<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>1.36858238253106<\/td>\n<td>1.37802461354736<\/td>\n<td>0.009442231<\/td>\n<td>1\/3.961<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>1.37565843490021<\/td>\n<td>1.37802461354736<\/td>\n<td>0.002366179<\/td>\n<td>1\/3.990<\/td>\n<\/tr>\n<tr>\n<td>16<\/td>\n<td>1.37743271822098<\/td>\n<td>1.37802461354736<\/td>\n<td>0.000591895<\/td>\n<td>1\/3.997<\/td>\n<\/tr>\n<tr>\n<td>32<\/td>\n<td>1.37787661780930<\/td>\n<td>1.37802461354736<\/td>\n<td>0.000147996<\/td>\n<td>1\/3.999<\/td>\n<\/tr>\n<\/table>\n<\/div>\n\u53ce\u675f\u7387\u306f\u307b\u307c 1\/4 \u306b\u306a\u3063\u3066\u304a\u308a, \u300c9.1.2 \u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206\u300d\u3067\u793a\u3057\u305f\u53ce\u675f\u7387\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b.<\/p>\n<p>\u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206\u306f\u7c21\u5358\u306a\u4ed5\u7d44\u307f\u3067, \u53f0\u5f62\u5247\u3084\u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u3068\u6bd4\u3079\u308b\u3068\u624b\u9593\u306f\u3042\u307e\u308a\u5909\u308f\u3089\u306a\u3044\u304c\u7cbe\u5ea6\u306f\u3088\u3044\u306e\u3067, \u3053\u308c\u3092\u4f7f\u3046\u4fa1\u5024\u306f\u3042\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (2) \u7a4d\u5206\u533a\u9593\u5916\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u95a2\u6570<\/h4>\n<p>\u7a4d\u5206\u533a\u9593\u5916\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u6b21\u306e\u95a2\u6570\u306e\u7a4d\u5206\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\nI = \\int_0^4 \\frac{1}{1 + x} dx = ln(1 + 4) = ln(5)<br \/>\n\\]\n\u6b21\u306e\u3088\u3046\u306b\u7a4d\u5206\u533a\u9593 [0, 4] \u3067\u306f\u6ed1\u3089\u304b\u306a\u95a2\u6570\u306b\u898b\u3048\u308b\u304c, \u8fd1\u304f\u306e x = -1 \u306b\u7279\u7570\u70b9\u3092\u6301\u3064.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_2_exp2_F.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5883\" \/><\/p>\n<p>\u3053\u308c\u3092\u4e0a\u3068\u540c\u3058\u3088\u3046\u306b\u7a2e\u3005\u306e\u7a4d\u5206\u516c\u5f0f\u3067\u8a08\u7b97\u3057\u8aa4\u5dee\u3092\u5bfe\u6570\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_2_exp2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5884\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_2_exp2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_2_exp2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u56f3\u306e\u3088\u3046\u306b\u3069\u306e\u516c\u5f0f\u3067\u3082\u7cbe\u5ea6\u304c\u843d\u3061\u305f\u306e\u304c\u308f\u304b\u308b. \u30ac\u30a6\u30b9\u516c\u5f0f\u3067\u3082 N = 18 \u4ee5\u4e0a\u3067\u306a\u3044\u3068\u6700\u9ad8\u7cbe\u5ea6\u306f\u5f97\u3089\u308c\u306a\u3044. \u7a4d\u5206\u533a\u9593\u5916\u306e\u7279\u7570\u70b9\u304c\u8a08\u7b97\u7cbe\u5ea6\u306b\u660e\u3089\u304b\u306b\u5f71\u97ff\u3057\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (3) \u8907\u7d20\u5e73\u9762\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u95a2\u6570<\/h4>\n<p>\u6b21\u306b\u4ee5\u4e0b\u306e\u7a4d\u5206\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\nI = \\int_0^4 \\frac{1}{1 + x^2} dx = arctan(4)<br \/>\n\\]\n\u3053\u308c\u306f\u5b9f\u6570\u8ef8\u4e0a\u306b\u306f\u7279\u7570\u70b9\u304c\u306a\u3044\u304c, \u8907\u7d20\u5e73\u9762\u3067\u306f\u8fd1\u304f(x = i) \u306b\u7279\u7570\u70b9\u304c\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_3_exp3_F.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5887\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_3_exp3_F.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_3_exp3_F-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u308c\u3092\u4e0a\u3068\u540c\u3058\u3088\u3046\u306b\u7a2e\u3005\u306e\u7a4d\u5206\u516c\u5f0f\u3067\u8a08\u7b97\u3057\u8aa4\u5dee\u3092\u5bfe\u6570\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_3_exp3.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5888\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_3_exp3.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_3_exp3-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u308c\u3082\u4e00\u3064\u524d\u306e\u4f8b\u3068\u540c\u3058\u3088\u3046\u306b\u3069\u306e\u516c\u5f0f\u3067\u3082\u7cbe\u5ea6\u304c\u843d\u3061\u305f. \u8907\u7d20\u5e73\u9762\u306e\u7279\u7570\u70b9\u3082\u5f71\u97ff\u3059\u308b\u306e\u304c\u308f\u304b\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (4) \u7aef\u70b9\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u95a2\u6570<\/h4>\n<p>\u6b21\u306b\u7aef\u70b9\u306b\u7279\u7570\u70b9\u304c\u3042\u308b\u3068\u3069\u3046\u306a\u308b\u304b\u898b\u3066\u307f\u308b.<br \/>\n\\[<br \/>\nI = \\int_0^1 \\sqrt{1 &#8211; x^2} dx = \\frac{\\pi}{4}<br \/>\n\\]\nx = 1 \u304c\u7279\u7570\u70b9\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_4_exp4_F.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5890\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_4_exp4_F.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_4_exp4_F-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u308c\u3092\u4e0a\u3068\u540c\u3058\u3088\u3046\u306b\u7a2e\u3005\u306e\u7a4d\u5206\u516c\u5f0f\u3067\u8a08\u7b97\u3057\u8aa4\u5dee\u3092\u5bfe\u6570\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_4_exp4.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5891\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_4_exp4.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_4_exp4-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u7aef\u70b9\u3068\u306f\u3044\u3048\u533a\u9593\u5185\u306b\u7279\u7570\u70b9\u304c\u3042\u308b\u5834\u5408\u306b\u306f\u3069\u306e\u516c\u5f0f\u3067\u3082\u7cbe\u5ea6\u304c\u5f97\u3089\u308c\u306a\u304b\u3063\u305f.<\/p>\n<p>\u3053\u306e\u4f8b\u306b\u304a\u3051\u308b\u53f0\u5f62\u5247\u306e\u53ce\u675f\u7387\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<br \/>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tr>\n<th>\u5206\u70b9\u6570<\/th>\n<th>\u7a4d\u5206\u5024(\u8a08\u7b97\u5024)<\/th>\n<th>\u7a4d\u5206\u5024(\u771f\u5024)<\/th>\n<th>\u8aa4\u5dee<\/th>\n<th>\u53ce\u675f\u7387<\/th>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>0.683012701892219<\/td>\n<td>0.785398163397448<\/td>\n<td>0.10238546<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0.748927267025610<\/td>\n<td>0.785398163397448<\/td>\n<td>0.036470896<\/td>\n<td>1\/2.807<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>0.772454786089293<\/td>\n<td>0.785398163397448<\/td>\n<td>0.012943377<\/td>\n<td>1\/2.818<\/td>\n<\/tr>\n<tr>\n<td>16<\/td>\n<td>0.780813259456935<\/td>\n<td>0.785398163397448<\/td>\n<td>0.0045849039<\/td>\n<td>1\/2.823<\/td>\n<\/tr>\n<tr>\n<td>32<\/td>\n<td>0.783775605719283<\/td>\n<td>0.785398163397448<\/td>\n<td>0.0016225577<\/td>\n<td>1\/2.826<\/td>\n<\/tr>\n<\/table>\n<\/div>\n\u53ce\u675f\u7387\u306f 1\/4 \u3067\u306f\u306a\u304f 1\/2.8 \u306b\u3057\u304b\u306a\u3063\u3066\u304a\u3089\u305a, \u6b63\u5e38\u306a\u52d5\u304d\u3092\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u308b. \u3053\u308c\u306b\u4f34\u3063\u3066\u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206\u306e\u52a0\u901f\u306e\u52b9\u679c\u304c\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b.<\/p>\n<h3>9.1.3.2 \u7121\u9650\u533a\u9593, \u534a\u7121\u9650\u533a\u9593\u306e\u7a4d\u5206<\/h3>\n<h4>\u6570\u5024\u5b9f\u9a13 (5) \u534a\u7121\u9650\u533a\u9593\u306e\u7a4d\u5206<\/h4>\n<p>\u6b21\u306e\u7a4d\u5206\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\nI = \\int_a^{\\infty} \\frac{e^{-x}}{x} = E1(a)<br \/>\n\\]\nE1(a) \u306f\u3088\u304f\u4f7f\u308f\u308c\u308b\u7279\u6b8a\u95a2\u6570\u306e\u3072\u3068\u3064\u306e\u6307\u6570\u7a4d\u5206\u3067\u3042\u308b. \u30b0\u30e9\u30d5\u306b\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306a\u5f62\u3092\u3057\u3066\u3044\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_5_exp5_F.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5893\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_5_exp5_F.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_5_exp5_F-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f\u306b\u3088\u308b a = 1 \u306e\u3068\u304d (E1(1)) \u306e\u8a08\u7b97\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_5_exp5.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5894\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_5_exp5.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_5_exp5-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (6) \u7121\u9650\u533a\u9593\u306e\u7a4d\u5206<\/h4>\n<p>\u6b21\u306e\u7a4d\u5206\u3092\u8003\u3048\u308b.<br \/>\n\\[<br \/>\nI = \\int_{-\\infty}^{+\\infty} \\frac{e^{-x^2}}{1 + x^2} = 1.3432934216<br \/>\n\\]\n\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_6_exp6_F.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5895\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_6_exp6_F.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_6_exp6_F-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f\u306b\u3088\u308b\u8a08\u7b97\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_6_exp6.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5896\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_6_exp6.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/9-1_6_exp6-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h3>9.1.4 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868<\/h3>\n<h3>(1) \u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f<\/h3>\n<p>\\[<br \/>\n\\begin{align}<br \/>\n&#038; \\int_a^b f(x) dx = h \\sum_{k=0}^n w_k f(x_k) \\\\<br \/>\n&#038; \u305f\u3060\u3057, h = \\frac{b &#8211; a}{n} \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u306b\u304a\u3051\u308b\u4fc2\u6570 \\(w_i\\) \u3092\u4ee5\u4e0b\u306b\u793a\u3059. \u672c\u6587\u3067\u8aac\u660e\u3057\u305f\u5f0f\u3092\u6570\u5f0f\u51e6\u7406\u30bd\u30d5\u30c8\u3092\u4f7f\u3063\u3066\u6709\u7406\u6570\u306e\u307e\u307e\u8a08\u7b97\u3057\u305f.<\/p>\n<pre>  \r\n         1  1\r\nnc(1) = [-, -]\r\n         2  2\r\n\r\n         1  4  1\r\nnc(2) = [-, -, -]\r\n         3  3  3\r\n\r\n         3  9  9  3\r\nnc(3) = [-, -, -, -]\r\n         8  8  8  8\r\n\r\n         14  64  8   64  14\r\nnc(4) = [--, --, --, --, --]\r\n         45  45  15  45  45\r\n\r\n         95   125  125  125  125  95\r\nnc(5) = [---, ---, ---, ---, ---, ---]\r\n         288  96   144  144  96   288\r\n\r\n         41   54  27   68  27   54  41\r\nnc(6) = [---, --, ---, --, ---, --, ---]\r\n         140  35  140  35  140  35  140\r\n\r\n         5257   25039  343  20923  20923  343  25039  5257\r\nnc(7) = [-----, -----, ---, -----, -----, ---, -----, -----]\r\n         17280  17280  640  17280  17280  640  17280  17280\r\n\r\n         3956   23552    3712   41984    3632  41984    3712   23552  3956\r\nnc(8) = [-----, -----, - -----, -----, - ----, -----, - -----, -----, -----]\r\n         14175  14175    14175  14175    2835  14175    14175  14175  14175\r\n\r\n         25713  141669  243   10881  26001  26001  10881  243   141669  25713\r\nnc(9) = [-----, ------, ----, -----, -----, -----, -----, ----, ------, -----]\r\n         89600  89600   2240  5600   44800  44800  5600   2240  89600   89600\r\n\r\n          80335   132875    80875  28375    24125  89035    24125  28375    80875  132875  80335\r\nnc(10) = [------, ------, - -----, -----, - -----, -----, - -----, -----, - -----, ------, ------]\r\n          299376  74844     99792  6237     5544   12474    5544   6237     99792  74844   299376\r\n\r\n<\/pre>\n<p>&nbsp;<\/p>\n<h3>(2) \u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f<\/h3>\n<p>\\[<br \/>\n\\int_a^b f(x) dx = \\frac{b &#8211; a}{N} \\sum_{i=1}^N f(\\frac{a + b}{2} + \\frac{(b &#8211; a)x_i}{2})<br \/>\n\\]\n\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u516c\u5f0f\u306b\u304a\u3051\u308b\u5206\u70b9 \\(x_i\\) \u3092\u4ee5\u4e0b\u306b\u793a\u3059. \u62e1\u5f35\u500d\u7cbe\u5ea6 (80 \u30d3\u30c3\u30c8\u6d6e\u52d5\u5c0f\u6570) \u306e\u8a08\u7b97\u306b\u3088\u308a\u672c\u6587\u3067\u8aac\u660e\u3057\u305f\u591a\u9805\u5f0f\u306e\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6c42\u3081, \u7d50\u679c\u306e 16 \u6841\u3092\u8868\u793a\u3057\u305f.<\/p>\n<pre>  \r\nN = 2\r\n  xi: -5.773502691896258E-0001  5.773502691896258E-0001\r\nN = 3\r\n  xi: -7.071067811865475E-0001  0.000000000000000E+0000  7.071067811865475E-0001\r\nN = 4\r\n  xi: -7.946544722917661E-0001 -1.875924740850799E-0001  1.875924740850799E-0001\r\n       7.946544722917661E-0001\r\nN = 5\r\n  xi: -8.324974870009819E-0001 -3.745414095535811E-0001  0.000000000000000E+0000\r\n       3.745414095535811E-0001  8.324974870009819E-0001\r\nN = 6\r\n  xi: -8.662468181078206E-0001 -4.225186537611115E-0001 -2.666354015167047E-0001\r\n       2.666354015167047E-0001  4.225186537611115E-0001  8.662468181078206E-0001\r\nN = 7\r\n  xi: -8.838617007580490E-0001 -5.296567752851568E-0001 -3.239118105199076E-0001\r\n       0.000000000000000E+0000  3.239118105199076E-0001  5.296567752851568E-0001\r\n       8.838617007580490E-0001\r\nN = 9\r\n  xi: -9.115893077284345E-0001 -6.010186553802381E-0001 -5.287617830578800E-0001\r\n      -1.679061842148039E-0001  0.000000000000000E+0000  1.679061842148039E-0001\r\n       5.287617830578800E-0001  6.010186553802381E-0001  9.115893077284345E-0001\r\n\r\n<\/pre>\n<p>&nbsp;<\/p>\n<h3>(3) \u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f (\u30ac\u30a6\u30b9\u516c\u5f0f)<\/h3>\n<p>\\[<br \/>\n\\int_a^b f(x) dx = \\frac{(b &#8211; a}{2} \\sum_{k=1}^N w_kf(\\frac{a + b}{2} + \\frac{b &#8211; a}{2}x_k)<br \/>\n\\]\n\u30ac\u30a6\u30b9\u30fb\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u516c\u5f0f\u306b\u304a\u3051\u308b\u5206\u70b9 \\(x_i\\) \u304a\u3088\u3073\u91cd\u307f \\(w_i\\) \u3092\u4ee5\u4e0b\u306b\u793a\u3059. \u5206\u70b9\u3068\u3057\u3066\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f\u306e\u30bc\u30ed\u70b9\u3092\u6c42\u3081, \u305d\u308c\u304b\u3089\u91cd\u307f\u3092\u8a08\u7b97\u3057\u305f. \u8a08\u7b97\u306f\u62e1\u5f35\u500d\u7cbe\u5ea6 (80 \u30d3\u30c3\u30c8\u6d6e\u52d5\u5c0f\u6570) \u306b\u3088\u308a\u884c\u3044\u7d50\u679c\u306e 16 \u6841\u3092\u8868\u793a\u3057\u305f.<\/p>\n<pre>  \r\nN = 2\r\n  xi: -5.773502691896258E-0001  5.773502691896258E-0001\r\n  wi:  1.000000000000000E+0000  1.000000000000000E+0000\r\nN = 3\r\n  xi: -7.745966692414834E-0001  0.000000000000000E+0000  7.745966692414834E-0001\r\n  wi:  5.555555555555556E-0001  8.888888888888889E-0001  5.555555555555556E-0001\r\nN = 4\r\n  xi: -8.611363115940526E-0001 -3.399810435848563E-0001  3.399810435848563E-0001\r\n       8.611363115940526E-0001\r\n  wi:  3.478548451374539E-0001  6.521451548625461E-0001  6.521451548625461E-0001\r\n       3.478548451374539E-0001\r\nN = 5\r\n  xi: -9.061798459386640E-0001 -5.384693101056831E-0001  0.000000000000000E+0000\r\n       5.384693101056831E-0001  9.061798459386640E-0001\r\n  wi:  2.369268850561891E-0001  4.786286704993665E-0001  5.688888888888889E-0001\r\n       4.786286704993665E-0001  2.369268850561891E-0001\r\nN = 6\r\n  xi: -9.324695142031520E-0001 -6.612093864662645E-0001 -2.386191860831969E-0001\r\n       2.386191860831969E-0001  6.612093864662645E-0001  9.324695142031520E-0001\r\n  wi:  1.713244923791703E-0001  3.607615730481386E-0001  4.679139345726910E-0001\r\n       4.679139345726910E-0001  3.607615730481386E-0001  1.713244923791703E-0001\r\nN = 7\r\n  xi: -9.491079123427585E-0001 -7.415311855993944E-0001 -4.058451513773972E-0001\r\n       0.000000000000000E+0000  4.058451513773972E-0001  7.415311855993944E-0001\r\n       9.491079123427585E-0001\r\n  wi:  1.294849661688697E-0001  2.797053914892767E-0001  3.818300505051189E-0001\r\n       4.179591836734694E-0001  3.818300505051189E-0001  2.797053914892767E-0001\r\n       1.294849661688697E-0001\r\nN = 8\r\n  xi: -9.602898564975362E-0001 -7.966664774136267E-0001 -5.255324099163290E-0001\r\n      -1.834346424956498E-0001  1.834346424956498E-0001  5.255324099163290E-0001\r\n       7.966664774136267E-0001  9.602898564975362E-0001\r\n  wi:  1.012285362903763E-0001  2.223810344533745E-0001  3.137066458778873E-0001\r\n       3.626837833783620E-0001  3.626837833783620E-0001  3.137066458778873E-0001\r\n       2.223810344533745E-0001  1.012285362903763E-0001\r\nN = 9\r\n  xi: -9.681602395076261E-0001 -8.360311073266358E-0001 -6.133714327005904E-0001\r\n      -3.242534234038089E-0001  0.000000000000000E+0000  3.242534234038089E-0001\r\n       6.133714327005904E-0001  8.360311073266358E-0001  9.681602395076261E-0001\r\n  wi:  8.127438836157441E-0002  1.806481606948574E-0001  2.606106964029355E-0001\r\n       3.123470770400028E-0001  3.302393550012598E-0001  3.123470770400028E-0001\r\n       2.606106964029355E-0001  1.806481606948574E-0001  8.127438836157441E-0002\r\nN = 10\r\n  xi: -9.739065285171717E-0001 -8.650633666889845E-0001 -6.794095682990244E-0001\r\n      -4.333953941292472E-0001 -1.488743389816312E-0001  1.488743389816312E-0001\r\n       4.333953941292472E-0001  6.794095682990244E-0001  8.650633666889845E-0001\r\n       9.739065285171717E-0001\r\n  wi:  6.667134430868814E-0002  1.494513491505806E-0001  2.190863625159820E-0001\r\n       2.692667193099964E-0001  2.955242247147529E-0001  2.955242247147529E-0001\r\n       2.692667193099964E-0001  2.190863625159820E-0001  1.494513491505806E-0001\r\n       6.667134430868814E-0002\r\n\r\n<\/pre>\n<p>&nbsp;<\/p>\n<h3>(4) \u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f<\/h3>\n<p>\\[<br \/>\n\\int_0^{\\infty} f(x)e^{-x} dx = \\sum_{k=1}^N w_k f(x_k)<br \/>\n\\]\n\u30ac\u30a6\u30b9\u30fb\u30e9\u30b2\u30fc\u30eb\u516c\u5f0f\u306b\u304a\u3051\u308b\u5206\u70b9 \\(x_i\\) \u304a\u3088\u3073\u91cd\u307f \\(w_i\\) \u3092\u4ee5\u4e0b\u306b\u793a\u3059. \u5206\u70b9\u3068\u3057\u3066\u30e9\u30b2\u30fc\u30eb\u591a\u9805\u5f0f\u306e\u30bc\u30ed\u70b9\u3092\u6c42\u3081, \u305d\u308c\u304b\u3089\u91cd\u307f\u3092\u8a08\u7b97\u3057\u305f. \u8a08\u7b97\u306f\u62e1\u5f35\u500d\u7cbe\u5ea6 (80 \u30d3\u30c3\u30c8\u6d6e\u52d5\u5c0f\u6570) \u306b\u3088\u308a\u884c\u3044\u7d50\u679c\u306e 16 \u6841\u3092\u8868\u793a\u3057\u305f.<\/p>\n<pre>  \r\nN = 2\r\n  xi: 5.857864376269050E-0001 3.414213562373095E+0000\r\n  wi: 8.535533905932738E-0001 1.464466094067262E-0001\r\nN = 3\r\n  xi: 4.157745567834791E-0001 2.294280360279042E+0000 6.289945082937479E+0000\r\n  wi: 7.110930099291730E-0001 2.785177335692408E-0001 1.038925650158614E-0002\r\nN = 4\r\n  xi: 3.225476896193923E-0001 1.745761101158347E+0000 4.536620296921128E+0000\r\n      9.395070912301133E+0000\r\n  wi: 6.031541043416336E-0001 3.574186924377997E-0001 3.888790851500538E-0002\r\n      5.392947055613275E-0004\r\nN = 5\r\n  xi: 2.635603197181409E-0001 1.413403059106517E+0000 3.596425771040722E+0000\r\n      7.085810005858838E+0000 1.264080084427578E+0001\r\n  wi: 5.217556105828087E-0001 3.986668110831759E-0001 7.594244968170760E-0002\r\n      3.611758679922048E-0003 2.336997238577623E-0005\r\nN = 6\r\n  xi: 2.228466041792607E-0001 1.188932101672623E+0000 2.992736326059314E+0000\r\n      5.775143569104511E+0000 9.837467418382590E+0000 1.598287398060170E+0001\r\n  wi: 4.589646739499636E-0001 4.170008307721210E-0001 1.133733820740450E-0001\r\n      1.039919745314907E-0002 2.610172028149321E-0004 8.985479064296212E-0007\r\nN = 7\r\n  xi: 1.930436765603624E-0001 1.026664895339192E+0000 2.567876744950746E+0000\r\n      4.900353084526485E+0000 8.182153444562861E+0000 1.273418029179781E+0001\r\n      1.939572786226254E+0001\r\n  wi: 4.093189517012739E-0001 4.218312778617198E-0001 1.471263486575053E-0001\r\n      2.063351446871694E-0002 1.074010143280746E-0003 1.586546434856420E-0005\r\n      3.170315478995581E-0008\r\nN = 8\r\n  xi: 1.702796323051010E-0001 9.037017767993799E-0001 2.251086629866131E+0000\r\n      4.266700170287659E+0000 7.045905402393466E+0000 1.075851601018100E+0001\r\n      1.574067864127800E+0001 2.286313173688926E+0001\r\n  wi: 3.691885893416375E-0001 4.187867808143430E-0001 1.757949866371718E-0001\r\n      3.334349226121565E-0002 2.794536235225673E-0003 9.076508773358213E-0005\r\n      8.485746716272532E-0007 1.048001174871510E-0009\r\nN = 9\r\n  xi: 1.523222277318082E-0001 8.072200227422558E-0001 2.005135155619347E+0000\r\n      3.783473973331233E+0000 6.204956777876613E+0000 9.372985251687576E+0000\r\n      1.346623691109209E+0001 1.883359778899170E+0001 2.637407189092738E+0001\r\n  wi: 3.361264217979625E-0001 4.112139804239844E-0001 1.992875253708856E-0001\r\n      4.746056276565160E-0002 5.599626610794583E-0003 3.052497670932106E-0004\r\n      6.592123026075352E-0006 4.110769330349548E-0008 3.290874030350708E-0011\r\nN = 10\r\n  xi: 1.377934705404924E-0001 7.294545495031705E-0001 1.808342901740316E+0000\r\n      3.401433697854900E+0000 5.552496140063804E+0000 8.330152746764497E+0000\r\n      1.184378583790007E+0001 1.627925783137810E+0001 2.199658581198076E+0001\r\n      2.992069701227389E+0001\r\n  wi: 3.084411157650201E-0001 4.011199291552736E-0001 2.180682876118094E-0001\r\n      6.208745609867775E-0002 9.501516975181101E-0003 7.530083885875388E-0004\r\n      2.825923349599566E-0005 4.249313984962686E-0007 1.839564823979631E-0009\r\n      9.911827219609009E-0013\r\n\r\n<\/pre>\n<p>&nbsp;<\/p>\n<h3>(5) \u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f<\/h3>\n<p>\\[<br \/>\n\\int_{-\\infty}^{+\\infty} f(x) e^{-x^2} dx = \\sum_{k=1}^N w_k f(x_k)<br \/>\n\\]\n\u30ac\u30a6\u30b9\u30fb\u30a8\u30eb\u30df\u30fc\u30c8\u516c\u5f0f\u306b\u304a\u3051\u308b\u5206\u70b9 \\(x_i\\) \u304a\u3088\u3073\u91cd\u307f \\(w_i\\) \u3092\u4ee5\u4e0b\u306b\u793a\u3059. \u5206\u70b9\u3068\u3057\u3066\u30a8\u30eb\u30df\u30fc\u30c8\u591a\u9805\u5f0f\u306e\u30bc\u30ed\u70b9\u3092\u6c42\u3081, \u305d\u308c\u304b\u3089\u91cd\u307f\u3092\u8a08\u7b97\u3057\u305f. \u8a08\u7b97\u306f\u62e1\u5f35\u500d\u7cbe\u5ea6 (80 \u30d3\u30c3\u30c8\u6d6e\u52d5\u5c0f\u6570) \u306b\u3088\u308a\u884c\u3044\u7d50\u679c\u306e 16 \u6841\u3092\u8868\u793a\u3057\u305f.<\/p>\n<pre>  \r\nN = 2\r\n  xi: -7.071067811865475E-0001  7.071067811865475E-0001\r\n  wi:  8.862269254527580E-0001  8.862269254527580E-0001\r\nN = 3\r\n  xi: -1.224744871391589E+0000  0.000000000000000E+0000  1.224744871391589E+0000\r\n  wi:  2.954089751509193E-0001  1.181635900603677E+0000  2.954089751509193E-0001\r\nN = 4\r\n  xi: -1.650680123885785E+0000 -5.246476232752903E-0001  5.246476232752903E-0001\r\n       1.650680123885785E+0000\r\n  wi:  8.131283544724518E-0002  8.049140900055128E-0001  8.049140900055128E-0001\r\n       8.131283544724518E-0002\r\nN = 5\r\n  xi: -2.020182870456086E+0000 -9.585724646138185E-0001  0.000000000000000E+0000\r\n       9.585724646138185E-0001  2.020182870456086E+0000\r\n  wi:  1.995324205904591E-0002  3.936193231522412E-0001  9.453087204829419E-0001\r\n       3.936193231522412E-0001  1.995324205904591E-0002\r\nN = 6\r\n  xi: -2.350604973674492E+0000 -1.335849074013697E+0000 -4.360774119276165E-0001\r\n       4.360774119276165E-0001  1.335849074013697E+0000  2.350604973674492E+0000\r\n  wi:  4.530009905508846E-0003  1.570673203228566E-0001  7.246295952243925E-0001\r\n       7.246295952243925E-0001  1.570673203228566E-0001  4.530009905508846E-0003\r\nN = 7\r\n  xi: -2.651961356835233E+0000 -1.673551628767471E+0000 -8.162878828589647E-0001\r\n       0.000000000000000E+0000  8.162878828589647E-0001  1.673551628767471E+0000\r\n       2.651961356835233E+0000\r\n  wi:  9.717812450995192E-0004  5.451558281912703E-0002  4.256072526101278E-0001\r\n       8.102646175568073E-0001  4.256072526101278E-0001  5.451558281912703E-0002\r\n       9.717812450995192E-0004\r\nN = 8\r\n  xi: -2.930637420257244E+0000 -1.981656756695843E+0000 -1.157193712446780E+0000\r\n      -3.811869902073221E-0001  3.811869902073221E-0001  1.157193712446780E+0000\r\n       1.981656756695843E+0000  2.930637420257244E+0000\r\n  wi:  1.996040722113676E-0004  1.707798300741348E-0002  2.078023258148919E-0001\r\n       6.611470125582413E-0001  6.611470125582413E-0001  2.078023258148919E-0001\r\n       1.707798300741348E-0002  1.996040722113676E-0004\r\nN = 9\r\n  xi: -3.190993201781528E+0000 -2.266580584531843E+0000 -1.468553289216668E+0000\r\n      -7.235510187528376E-0001  0.000000000000000E+0000  7.235510187528376E-0001\r\n       1.468553289216668E+0000  2.266580584531843E+0000  3.190993201781528E+0000\r\n  wi:  3.960697726326438E-0005  4.943624275536947E-0003  8.847452739437657E-0002\r\n       4.326515590025558E-0001  7.202352156060510E-0001  4.326515590025558E-0001\r\n       8.847452739437657E-0002  4.943624275536947E-0003  3.960697726326438E-0005\r\nN = 10\r\n  xi: -3.436159118837738E+0000 -2.532731674232790E+0000 -1.756683649299882E+0000\r\n      -1.036610829789514E+0000 -3.429013272237046E-0001  3.429013272237046E-0001\r\n       1.036610829789514E+0000  1.756683649299882E+0000  2.532731674232790E+0000\r\n       3.436159118837738E+0000\r\n  wi:  7.640432855232621E-0006  1.343645746781233E-0003  3.387439445548106E-0002\r\n       2.401386110823147E-0001  6.108626337353258E-0001  6.108626337353258E-0001\r\n       2.401386110823147E-0001  3.387439445548106E-0002  1.343645746781233E-0003\r\n       7.640432855232621E-0006\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>9.1.1 \u57fa\u672c\u7684\u306a\u7a4d\u5206\u516c\u5f0f \u7a4d\u5206\u533a\u9593 [a, b] \u3092 n \u5206\u5272\u3059\u308b\u5206\u70b9\u5217\u3092 \\(a = x_0 < x_1 < \\dots < x_n = b\\), \u5404\u5206\u70b9\u306b\u304a\u3051\u308b\u91cd\u307f\u3092 \\(w_i\\), 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