{"id":5899,"date":"2026-07-17T11:05:17","date_gmt":"2026-07-17T02:05:17","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=5899"},"modified":"2026-07-17T11:05:17","modified_gmt":"2026-07-17T02:05:17","slug":"9-2_quad","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/9-2_quad\/","title":{"rendered":"9.2 \u5909\u6570\u5909\u63db\u578b\u7a4d\u5206\u516c\u5f0f, \u9069\u5fdc\u81ea\u52d5\u7a4d\u5206"},"content":{"rendered":"\n

9.2.1 \u53f0\u5f62\u5247\u306e\u8aa4\u5dee<\/h3>\n

\u53f0\u5f62\u5247\u3067\u306f\u5206\u70b9\u6570\u3092\u500d (\u523b\u307f\u5e45 h \u3092 1\/2) \u306b\u3059\u308b\u3068\u8aa4\u5dee\u306f\u304a\u304a\u3088\u305d 1\/4 \u306b\u306a\u3063\u305f. \u3053\u308c\u306f, \u88ab\u7a4d\u5206\u95a2\u6570\u304c\u89e3\u6790\u7684\u306a\u5834\u5408\u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u304c\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3053\u3068\u306b\u3088\u308b (\u30aa\u30a4\u30e9\u30fc\u30fb\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b).
\n\\[
\nI_m – I = c_2 h^2(f'(b) – f'(a)) + c_4 h^4(f”'(b) – f”'(a)) + \\dots + c_2p h^{2p}(f^{(2p-1)}(b) – f^{(2p-1)}(a)) + O(h^{2p+2})
\n\\]\n\u3053\u3053\u3067 \\(c_i\\) \u306f \\(h\\) \u3084 \\(f\\) \u306b\u7121\u95a2\u4fc2\u306a\u5b9a\u6570\u3067\u3042\u308b.<\/p>\n

\\(h^4\\) \u4ee5\u4e0a\u306e\u9805\u304c\u5341\u5206\u5c0f\u3055\u3044\u3068\u4eee\u5b9a\u3059\u308b\u3068\u8aa4\u5dee\u306f\u307b\u307c \\(h^2\\) \u306b\u6bd4\u4f8b\u3059\u308b\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d, \\(h\\) \u304c 1\/2 \u306b\u306a\u308b\u3068\u8aa4\u5dee\u306f 1\/4 \u306b\u306a\u308b. \u3057\u304b\u3057, \u5fae\u5206\u4e0d\u53ef\u80fd\u306a\u7279\u7570\u70b9\u304c\u3042\u3063\u305f\u308a\u3059\u308b\u3068\u3053\u308c\u304c\u6210\u308a\u7acb\u305f\u306a\u304f\u306a\u308b\u3053\u3068\u306f\u300c9.1.3 \u6570\u5024\u5b9f\u9a13\u300d\u3067\u898b\u305f.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (7) \u5468\u671f\u95a2\u6570<\/h4>\n

\u7279\u5225\u306a\u5834\u5408\u306e\u4f8b\u3068\u3057\u3066\u6b21\u306e\u95a2\u6570\u306e [0, \\(\\pi\\)\/2] \u3067\u306e\u7a4d\u5206\u3092\u6c42\u3081\u308b.
\n\\[
\nI = \\int_0^{\\pi\/2} \\frac{1}{\\sqrt{1 – sin^2(x) \/ 2}} dx = 1.85407467730137
\n\\]\n

\"\"<\/p>\n

\u56f3\u304b\u3089\u3082\u308f\u304b\u308b\u3088\u3046\u306b\u3053\u308c\u306f\u5468\u671f\u95a2\u6570\u3067\u3042\u308b. \u7a2e\u3005\u306e\u7a4d\u5206\u516c\u5f0f\u3067\u5206\u70b9\u6570 N (\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>\n

\u610f\u5916\u306b\u3082\u53f0\u5f62\u5247\u304c\u6700\u3082\u901f\u304f\u53ce\u675f\u3057\u3066\u3044\u308b. \u53f0\u5f62\u5247\u306e\u7d50\u679c\u3092\u8868\u306b\u3057\u3066\u307f\u308b\u3068, \u53ce\u675f\u7387 = 1\/4 \u3068\u6bd4\u8f03\u3059\u308b\u3068\u6841\u9055\u3044\u306b\u5c0f\u3055\u304f (\u53ce\u675f\u304c\u901f\u304f) \u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b. \u3053\u3046\u306a\u308b\u3068\u56f3\u306e\u3088\u3046\u306b\u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206\u306f\u304b\u3048\u3063\u3066\u9045\u304f\u306a\u308b.<\/p>\n

\n\n\n\n\n\n\n
\u5206\u70b9\u6570<\/th>\n\u7a4d\u5206\u5024(\u8a08\u7b97\u5024)<\/th>\n\u7a4d\u5206\u5024(\u771f\u5024)<\/th>\n\u8aa4\u5dee<\/th>\n\u53ce\u675f\u7387<\/th>\n<\/tr>\n
2<\/td>\n1.85495913108563<\/td>\n1.85407467730137<\/td>\n8.8445378e-4<\/td>\n<\/td>\n<\/tr>\n
4<\/td>\n1.85407522776731<\/td>\n1.85407467730137<\/td>\n5.5046594e-7<\/td>\n1\/1607<\/td>\n<\/tr>\n
8<\/td>\n1.85407467730167<\/td>\n1.85407467730137<\/td>\n2.9465319e-13<\/td>\n1\/1.868e+6<\/td>\n<\/tr>\n
16<\/td>\n1.85407467730137<\/td>\n1.85407467730137<\/td>\n0<\/td>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n\u3053\u308c\u306f, \u5468\u671f\u6027\u306e\u3042\u308b\u95a2\u6570\u306f\u305d\u306e\u4e21\u7aef\u3067\u5fae\u5206\u4fc2\u6570\u304c\u4e00\u81f4\u3057, \u4e0a\u5f0f (\u30aa\u30a4\u30e9\u30fc\u30fb\u30de\u30af\u30ed\u30fc\u30ea\u30f3\u5c55\u958b) \u3067\u8868\u3055\u308c\u308b\u8aa4\u5dee\u304c 0 \u306b\u8fd1\u304f\u306a\u308b\u305f\u3081\u3067\u3042\u308b. \u3053\u306e\u4f8b\u306f\u7a4d\u5206\u7bc4\u56f2\u304c\u534a\u5468\u671f\u3067\u3042\u308b\u304c\u5bfe\u79f0\u6027\u304c\u3042\u308b\u305f\u3081\u3053\u306e\u6761\u4ef6\u306b\u3042\u3066\u306f\u307e\u308b. \u3053\u306e\u3088\u3046\u306a\u5834\u5408\u306b\u306f\u53f0\u5f62\u5247\u304c\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (8) \u7121\u9650\u7a4d\u5206<\/h4>\n

\u3082\u3046\u3072\u3068\u3064, \u7121\u9650\u7a4d\u5206\u306e\u4f8b\u3092\u898b\u3066\u307f\u308b.
\n\\[
\n\\int_0^{\\infty} e^{-x^2\/2} dx = 1.25331413731550
\n\\]\n\u95a2\u6570\u5f62\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b. \u95a2\u6570\u5024\u306f x = 8 \u3067 \\(10^{-14}\\) \u306e\u30aa\u30fc\u30c0\u30fc, x = 10 \u3067 \\(10^{-22}\\) \u306e\u30aa\u30fc\u30c0\u30fc\u3068\u6025\u901f\u306b 0 \u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u95a2\u6570\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n

\"\"<\/p>\n

\u3053\u3053\u3067, \u7a4d\u5206\u7bc4\u56f2\u3092 \\([0, \\infty]\\) \u306e\u4ee3\u308f\u308a\u306b \\([0, 10]\\) \u3068\u3057\u3066\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n

\"\"<\/p>\n

\u3053\u3053\u3067\u3082\u53f0\u5f62\u5247\u304c\u4e00\u756a\u901f\u304f\u53ce\u675f\u3057, N = 15 \u3067\u6700\u9ad8\u7cbe\u5ea6\u306b\u9054\u3057\u305f.<\/p>\n

\u6e1b\u8870\u304c\u901f\u3044\u95a2\u6570\u3067\u306f\u7aef\u3067\u3059\u3050\u306b\u5fae\u5206\u4fc2\u6570\u304c 0 \u306b\u8fd1\u3065\u304f\u305f\u3081, \u4e0a\u5f0f\u3067\u8868\u3055\u308c\u308b\u8aa4\u5dee\u3082\u901f\u304f 0 \u306b\u8fd1\u3065\u304f\u3068\u8003\u3048\u3089\u308c\u308b. \u3053\u306e\u3088\u3046\u306a\u7121\u9650\u7a4d\u5206\u306b\u5bfe\u3057\u3066\u3082\u53f0\u5f62\u5247\u304c\u4ed6\u306e\u516c\u5f0f\u3088\u308a\u3082\u7cbe\u5ea6\u304c\u826f\u3044\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b.<\/p>\n

9.2.2 \u5909\u6570\u5909\u63db\u578b\u7a4d\u5206\u516c\u5f0f<\/h3>\n

\u53f0\u5f62\u5247\u306f\u5468\u671f\u6027\u306e\u3042\u308b\u95a2\u6570\u306e\u7a4d\u5206\u3084\u6e1b\u8870\u306e\u901f\u3044\u7121\u9650\u7a4d\u5206\u306b\u5bfe\u3057\u3066\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u304c, \u5b9f\u969b\u306b\u53f0\u5f62\u5247\u304c\u305d\u306e\u307e\u307e\u4f7f\u308f\u308c\u308b\u3053\u3068\u306f\u306a\u3044. \u3057\u304b\u3057, \u53f0\u5f62\u5247\u306e\u3053\u306e\u7279\u9577\u306f\u4ee5\u4e0b\u306b\u793a\u3059\u5909\u6570\u5909\u63db\u306b\u3088\u308b\u7a4d\u5206\u516c\u5f0f\u306b\u5fdc\u7528\u3055\u308c\u3066\u3044\u308b.<\/p>\n

\u4e00\u822c\u306e\u7a4d\u5206\u3092\u300c9.2.1 \u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u300d\u306e 2 \u3064\u306e\u30b1\u30fc\u30b9\u306e\u3088\u3046\u306b\u53f0\u5f62\u5247\u304c\u901f\u304f\u306a\u308b\u3088\u3046\u306a\u7a4d\u5206\u306b\u306a\u308b\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3057, \u305d\u308c\u306b\u53f0\u5f62\u5247\u3092\u9069\u7528\u3059\u308c\u3070\u6027\u80fd\u306e\u826f\u3044\u7a4d\u5206\u516c\u5f0f\u3068\u306a\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u308b. \u3053\u306e\u30a2\u30a4\u30c7\u30a2\u306b\u57fa\u3065\u304f\u516c\u5f0f\u304c\u5909\u6570\u5909\u63db\u578b\u7a4d\u5206\u516c\u5f0f\u3067\u3042\u308b.<\/p>\n

\u7a4d\u5206\u5909\u6570\u3092\u5909\u63db\u3059\u308b\u516c\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.
\n\\[
\n\\begin{align}
\n& \\int_a^b f(x)dx = \\int_c^d g(t)dt \\\\
\n& \u305f\u3060\u3057, \\space x = \\phi(t), \\space g(t) = f(\\phi(t))\\phi'(t) \\\\
\n\\end{align}
\n\\]\n\u3053\u3053\u3067 \\(\\phi(t)\\) \u306f\u533a\u9593 [c, d] \u3067\u5358\u8abf\u3067, \u304b\u3064 \\(a = \\phi(c), \\space b = \\phi(d)\\) \u3067\u3042\u308b. \u3053\u308c\u306b\u3088\u308a\u7a4d\u5206\u5024\u304c\u4e0d\u5909\u306e\u307e\u307e\u88ab\u7a4d\u5206\u95a2\u6570\u3092\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b. \u9069\u5207\u306a \\(\\phi(t)\\) \u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u52b9\u679c\u7684\u306a\u516c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n

9.2.2.1 IMT\u516c\u5f0f<\/h3>\n

\\(\\phi(t)\\) \u3068\u3057\u3066\u6b21\u5f0f\u3092\u4f7f\u3046\u306e\u304c IMT \u516c\u5f0f\u3067\u3042\u308b.
\n\\[
\n\\begin{align}
\n& \\phi(t) = \\frac{1}{Q} \\int_0^t \\psi(r) dr, \\space Q = \\int_0^1 \\psi(r) dr \\\\
\n& \u305f\u3060\u3057, \\space \\psi(r) = exp(\\frac{-1}{r} – \\frac{1}{1 – r}) \\\\
\n\\end{align}
\n\\]\n\u3053\u306e\u5909\u63db\u3092\u533a\u9593 [0, 1] \u306e\u7a4d\u5206\u306b\u9069\u7528\u3059\u308b\u3068, \u5909\u63db\u5f8c\u306e\u95a2\u6570 \\(g(t)\\) \u306f \\(g^{(j)}(0) = g^{(j)}(1) = 0 \\space (j = 0, 1, \\dots)\\) \u3068\u306a\u308b. \u3059\u306a\u308f\u3061, \u7a4d\u5206\u533a\u9593\u306e\u4e21\u7aef\u3067\u5fae\u5206\u4fc2\u6570\u304c 0 \u306b\u306a\u3063\u3066\u3044\u3066, \u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u304c 0 \u306b\u8fd1\u304f\u306a\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p>\n

\u3053\u306e\u5909\u63db\u3092\u65bd\u3057\u53f0\u5f62\u5247\u3092\u9069\u7528\u3059\u308b\u3068, \u5206\u70b9\u6570\u3092 N \u3068\u3057\u3066\u6b21\u306e\u8a08\u7b97\u5f0f\u304c\u5f97\u3089\u308c\u308b.
\n\\[
\n\\begin{align}
\n& S_N = \\frac{1}{N} \\sum_{i=1}^N w_i^{(N)} f(x_i^{(N)}) \\\\
\n& \u91cd\u307f: w_i^{(N)} = \\phi'(\\frac{i}{N}) = \\frac{1}{Q}\\psi(\\frac{i}{N}) \\\\
\n& \u5206\u70b9: x_i^{(N)} = \\phi(\\frac{i}{N}) = \\frac{1}{Q}\\int_0^{\\frac{i}{N}} \\psi(r) dr \\\\
\n\\end{align}
\n\\]\nIMT \u516c\u5f0f\u306b\u3064\u3044\u3066\u306f\u6587\u732e[3], [4]\u306b\u8a73\u3057\u3044.<\/p>\n

9.2.2.2 \u4e8c\u91cd\u6307\u6570\u578b\u7a4d\u5206\u516c\u5f0f (DE \u516c\u5f0f)<\/h3>\n

\u5bfe\u8c61\u3068\u3059\u308b\u7a4d\u5206\u3092\u6e1b\u8870\u306e\u901f\u3044\u7121\u9650\u7a4d\u5206\u306b\u5909\u63db\u3057\u3066\u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u304c 0 \u306b\u8fd1\u304f\u306a\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3053\u3068\u306b\u3088\u308a\u52b9\u7387\u3088\u304f\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u306e\u304c\u4e8c\u91cd\u6307\u6570\u578b\u7a4d\u5206\u516c\u5f0f (DE \u516c\u5f0f) \u3067\u3042\u308b. \u5909\u63db\u95a2\u6570 \\(\\phi(t)\\) \u306f\u7a4d\u5206\u533a\u9593\u306a\u3069\u306b\u3088\u3063\u3066\u3044\u304f\u3064\u304b\u306e\u7a2e\u985e\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u308b.<\/p>\n

DE \u516c\u5f0f\u306b\u3064\u3044\u3066\u306f\u6587\u732e[2], [4], [5]\u306b\u8a73\u3057\u3044. \u5909\u6570\u5909\u63db\u578b\u7a4d\u5206\u516c\u5f0f\u3068\u3057\u3066\u306f IMT \u516c\u5f0f\u304c\u306f\u3058\u3081\u306b\u63d0\u6848\u3055\u308c, \u305d\u306e\u5f8c DE \u516c\u5f0f\u304c\u63d0\u6848\u3055\u308c\u305f. \u73fe\u5728\u3067\u306f\u4e3b\u306b DE \u516c\u5f0f\u304c\u4f7f\u308f\u308c\u3066\u3044\u308b.<\/p>\n

(1) \u6709\u9650\u533a\u9593 [-1, 1] \u306e\u7a4d\u5206<\/h4>\n

\\(\\phi(t)\\) \u3068\u3057\u3066\u6b21\u3092\u4f7f\u3046.
\n\\[
\n\\begin{align}
\n& S_h^{(N)} = h \\sum_{i=N_-}^{N_+} w_i^{(N)} f(x_i^{(N)}) \\\\
\n& \\phi(t) = tanh(\\frac{\\pi}{2}sinh(t)) \\\\
\n& \\phi'(t) = \\frac{\\frac{\\pi}{2}cosh(t)}{cosh^2(\\frac{\\pi}{2}sinh(t))} \\\\
\n\\end{align}
\n\\]\n\u304d\u3056\u307f\u3092 \\(h\\), \u5206\u70b9\u6570\u3092 \\(N (= N_+ + N_- + 1)\\) \u3068\u3059\u308b\u3068, \u8a08\u7b97\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.
\n\\[
\n\\begin{align}
\n& \u91cd\u307f: w_i^{(N)} = h \\phi'(ih) \\\\
\n& \u5206\u70b9: x_i^{(N)} = \\phi(ih) \\\\
\n\\end{align}
\n\\]\n\u7121\u9650\u7a4d\u5206\u306e\u8a08\u7b97\u306f\u4e0b\u5074\u3092 \\(-N_-\\), \u4e0a\u5074\u3092 \\(N_+\\) \u3067\u6253\u3061\u5207\u308b. \u3053\u308c\u3089\u306e\u5024\u306f\u8a31\u5bb9\u8aa4\u5dee\u9650\u754c\u3092\u3082\u3068\u306b\u9069\u5207\u306a\u5024\u3092\u8a2d\u5b9a\u3059\u308b.<\/p>\n

\u7aef\u70b9\u306b\u7279\u7570\u70b9\u304c\u3042\u308b\u95a2\u6570\u306e\u4f8b\u3067\u53d6\u308a\u4e0a\u3052\u305f \\(I = \\int_0^1 \\sqrt{1 – x^2} dx = \\pi\/4\\) \u306e\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u518d\u63b2\u3059\u308b. \u3053\u306e\u95a2\u6570\u306f\u4e0b\u306e\u6570\u5024\u5b9f\u9a13 (2) \u3067\u3082\u4f7f\u7528\u3059\u308b.<\/p>\n

\"\"<\/p>\n

\u3053\u308c\u3092\u4e0a\u306e\u5909\u63db\u95a2\u6570 \\(\\phi(t)\\) \u3092\u4f7f\u3063\u3066\u7121\u9650\u7a4d\u5206\u306b\u5909\u63db\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n

\"\"<\/p>\n

\u4e0a\u5074\u3082\u4e0b\u5074\u3082\u6e1b\u8870\u304c\u901f\u3044\u3053\u3068\u304c\u308f\u304b\u308b. \u304d\u3056\u307f\u5e45\u3092 0.1 \u3068\u3057\u3066\u3084\u308b\u3068, \u4e0a\u5074\u30fb\u4e0b\u5074\u305d\u308c\u305e\u308c 32 \u70b9\u3067 \\(10^{-15}\\) \u4ee5\u4e0b\u306e\u30aa\u30fc\u30c0\u30fc\u307e\u3067\u6e1b\u8870\u3057\u305f. \u3053\u308c\u306f\u53f0\u5f62\u5247\u3067\u7cbe\u5ea6\u3088\u304f\u7a4d\u5206\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n

(2) \u534a\u7121\u9650\u533a\u9593 [0, \\(\\infty\\)] \u306e\u7a4d\u5206<\/h4>\n

\u534a\u7121\u9650\u533a\u9593\u306e\u7a4d\u5206\u306b\u304a\u3044\u3066\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u3086\u308b\u3084\u304b\u306b\u6e1b\u8870\u3059\u308b\u3088\u3046\u306a\u5834\u5408\u306b\u3064\u3044\u3066\u3082\u6709\u9650\u533a\u9593\u306e\u5834\u5408\u3068\u540c\u69d8\u306e\u8003\u3048\u65b9\u3067 DE \u516c\u5f0f\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u308b. \u6587\u732e[2]\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u30d7\u30ed\u30b0\u30e9\u30e0 DEHINT \u3067\u306f\u88ab\u7a4d\u5206\u95a2\u6570\u306b\u3088\u308a 3 \u7a2e\u985e\u306e\u516c\u5f0f\u3092\u4f7f\u3044\u5206\u3051\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n

(a) \u901a\u5e38\u306e\u95a2\u6570\u306e\u5834\u5408
\n\\[
\n\\begin{align}
\n& \\phi(t) = exp(2sinh(t)) \\\\
\n& \\phi'(t) = 2cosh(t)exp(2sinh(t)) \\\\
\n\\end{align}
\n\\]\n(b) \u88ab\u7a4d\u5206\u95a2\u6570\u304c\u6307\u6570\u95a2\u6570\u7684\u306b\u6e1b\u8870\u3059\u308b\u5834\u5408 (\\(f(x) = f_1(x)exp(-x)\\) \u306e\u5f62\u3092\u3057\u3066\u3044\u308b\u5834\u5408)
\n\\[
\n\\begin{align}
\n& \\phi(t) = exp(t – e^{-t}) \\\\
\n& \\phi'(t) = (1 + e^{-t})exp(t – e^{-t}) \\\\
\n\\end{align}
\n\\]\n(c) \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u6e1b\u8870\u304c\u3055\u3089\u306b\u6025\u6fc0\u306a\u5834\u5408 (\\(f(x) = f_2(x)exp(-x^2)\\) \u306e\u5f62\u3092\u3057\u3066\u3044\u308b\u5834\u5408)
\n\\[
\n\\begin{align}
\n& \\phi(t) = exp(\\frac{t}{2} – e^{-t}) \\\\
\n& \\phi'(t) = (\\frac{1}{2} + e^{-t})exp(\\frac{t}{2} – e^{-t}) \\\\
\n\\end{align}
\n\\]\n

(3) \u5168\u7121\u9650\u533a\u9593 [\\(-\\infty\\), \\(+\\infty\\)] \u306e\u7a4d\u5206<\/h4>\n

\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u3086\u308b\u3084\u304b\u306b\u6e1b\u8870\u3059\u308b\u3088\u3046\u306a\u5168\u7121\u9650\u533a\u9593\u306e\u7a4d\u5206\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b DE \u516c\u5f0f\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u308b.
\n\\[
\n\\begin{align}
\n& \\phi(t) = sinh(\\frac{\\pi}{2}sinh(t)) \\\\
\n& \\phi'(t) = \\frac{\\pi}{2}cosh(t)cosh(\\frac{\\pi}{2}sinh(t)) \\\\
\n\\end{align}
\n\\]\n

(4) \u30d5\u30fc\u30ea\u30a8\u578b\u7a4d\u5206<\/h4>\n

\u6b21\u306e\u534a\u7121\u9650\u533a\u9593\u306e\u7a4d\u5206 (\u30d5\u30fc\u30ea\u30a8\u578b\u7a4d\u5206) \u3092\u6c42\u3081\u308b.
\n\\[
\nI_c = \\int_a^{\\infty} f(x) cos(\\omega x) dx \\space \u307e\u305f\u306f \\space I_s = \\int_a^{\\infty} f(x) sin(\\omega x) dx
\n\\]\n\u6b21\u306e\u5909\u63db\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u7121\u9650\u533a\u9593 [\\(-\\infty\\), \\(+\\infty\\)] \u306e\u7a4d\u5206\u306b\u5909\u63db\u3059\u308b.
\n\\[
\n\\begin{align}
\n& I_c \u306e\u5834\u5408: x = M \\phi(t – \\frac{\\pi}{2M})\/\\omega
\n& I_s \u306e\u5834\u5408: x = M \\phi(t)\/\\omega
\n\\end{align}
\n\\]\n\\(\\phi(t)\\) \u306f \\(t \\to -\\infty\\) \u306e\u3068\u304d\u306b\u4e8c\u91cd\u6307\u6570\u95a2\u6570\u7684\u306b \\(\\phi'(t) \\to 0, \\space t \\to +\\infty\\) \u306e\u3068\u304d\u306b\u4e8c\u91cd\u6307\u6570\u95a2\u6570\u7684\u306b \\(\\phi(t) \\to t\\) \u3068\u306a\u308b\u3088\u3046\u306a\u95a2\u6570\u3067\u3042\u308b. \u304d\u3056\u307f\u5e45 \\(h\\) \u3068\u5b9a\u6570 \\(M\\) \u306f, \\(Mh = \\pi\\) \u304c\u6210\u308a\u7acb\u3064\u3088\u3046\u306b\u9078\u3070\u308c\u308b. \u3053\u306e\u5909\u63db\u306b\u3088\u308a, x \u304c\u5927\u304d\u304f\u306a\u308b\u3068\u304d\u306b\u516c\u5f0f\u306e\u5206\u70b9\u304c \\(cos(\\omega x)\\) \u3042\u308b\u3044\u306f \\(sin(\\omega x)\\) \u306e\u30bc\u30ed\u70b9\u306b\u4e8c\u91cd\u6307\u6570\u95a2\u6570\u7684\u306b\u8fd1\u3065\u304f\u3088\u3046\u306b\u306a\u308a, \u5927\u304d\u306a x \u306b\u3064\u3044\u3066\u306f\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057\u306a\u304f\u3066\u3082\u3088\u304f\u306a\u308b.<\/p>\n

\u03c6(t)\u306f\u3044\u304f\u3064\u304b\u63d0\u6848\u3055\u308c\u3066\u3044\u308b\u304c, \u4f8b\u3048\u3070\u6b21\u5f0f\u304c\u3042\u308b.
\n\\[
\n\\begin{align}
\n& \\phi(t) = \\frac{t}{1 – exp(-ksinh(t))}, \\space k = 6 \\space (\u307e\u305f\u306f \\space 2\\pi) \\space (\u6587\u732e[4], [5], [7]) \\\\
\n& \u307e\u305f\u306f \\\\
\n& \\phi(t) = \\frac{t}{1 – exp(-2t -\\alpha(1 – e^{-t}) – \\beta(e^t – 1))}, \\space \\beta = \\frac{1}{4}, \\space \\alpha = \\frac{\\beta}{\\sqrt{1 + M log(1 + M)\/4\\pi}} \\space (\u6587\u732e[9]) \\\\
\n\\end{align}
\n\\]\n\u4e0b\u306e\u6570\u5024\u5b9f\u9a13 (11) \u3067\u4f7f\u7528\u3059\u308b \\(I = \\int_0^{\\infty} log(x)sin(x)dx = -\\gamma\\) \u306e\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u793a\u3059.<\/p>\n

\"\"<\/p>\n

\u6587\u732e[7]\u306e\u516c\u5f0f (\\(K = 2\\pi\\)) \u3092\u4f7f\u3044, \\(Tol = 10^{-5}\\) \u3068\u3057\u305f\u3068\u304d\u306e\u5206\u70b9\u3092\u8d64\u4e38\u3067\u793a\u3057\u305f. x \u304c\u5927\u304d\u304f\u306a\u308b\u3068\u5206\u70b9\u304c\u95a2\u6570\u306e\u30bc\u30ed\u70b9\u306b\u4e00\u81f4\u3057\u3066\u3044\u304f\u306e\u304c\u308f\u304b\u308b.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (9) \u6027\u8cea\u306e\u3088\u3044\u95a2\u6570<\/h4>\n

\u300c9.1.3.1 (1) \u6027\u8cea\u306e\u826f\u3044\u95a2\u6570\u300d\u3067\u5b9f\u9a13\u3057\u305f\u95a2\u6570\u3092\u7528\u3044\u3066\u5909\u6570\u5909\u63db\u578b\u516c\u5f0f\u306e\u6027\u80fd\u3092\u898b\u308b.<\/p>\n

\u6b21\u306e\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u3002
\n\\[
\nI = \\int_0^1 e^x cos(x) dx = 1.378024613547364
\n\\]\nDE \u516c\u5f0f\u3067\u306f\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u4f5c\u308a\u306b\u3088\u3063\u3066\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u304c\u5909\u308f\u3063\u3066\u304f\u308b\u304c, \u3053\u3053\u3067\u306f\u304d\u3056\u307f\u307f\u5e45\u3092\u5909\u5316\u3055\u305b\u3066\u305d\u306e\u3068\u304d\u306e\u5b9f\u969b\u306e\u7cbe\u5ea6\u306b\u307f\u3042\u3063\u305f\u3068\u3053\u308d\u3067\u7121\u9650\u7a4d\u5206\u3092\u6253\u3061\u5207\u308b\u3088\u3046\u306b\u3057\u305f (\u81ea\u52d5\u7a4d\u5206\u3067\u306f\u306a\u3044).<\/p>\n

\"\"<\/p>\n

\u6bd4\u8f03\u306e\u305f\u3081\u53f0\u5f62\u5247, \u30b7\u30f3\u30d7\u30bd\u30f3\u5247, \u30ac\u30a6\u30b9\u516c\u5f0f\u3082\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n

IMT \u516c\u5f0f\u306f\u307b\u307c\u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u306a\u307f\u306e\u6027\u80fd\u306b\u898b\u3048\u308b. DE \u516c\u5f0f\u306f IMT \u516c\u5f0f\u3088\u308a\u306f\u901f\u3044\u304c\u30ac\u30a6\u30b9\u516c\u5f0f\u307b\u3069\u3067\u306f\u306a\u3044.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (10) \u7aef\u70b9\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u95a2\u6570<\/h4>\n

\u300c9.1.3.1 (3) \u7aef\u70b9\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u95a2\u6570\u300d\u3067\u5b9f\u9a13\u3057\u305f\u7aef\u70b9\u306b\u7279\u7570\u70b9\u3092\u6301\u3064\u95a2\u6570\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u898b\u308b.
\n\\[
\nI = \\int_0^1 \\sqrt{1 – x^2} dx = \\frac{\\pi}{4}
\n\\]\nx = 1 \u306b\u7279\u7570\u70b9\u304c\u3042\u308b.<\/p>\n

\"\"<\/p>\n

\u524d\u306b\u793a\u3057\u305f\u3088\u3046\u306b\u88dc\u9593\u578b\u516c\u5f0f\u3067\u306f\u3069\u308c\u3082\u5341\u5206\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u306a\u304b\u3063\u305f\u304c, IMT \u516c\u5f0f\u3068 DE \u516c\u5f0f\u306f\u7279\u7570\u70b9\u306e\u5f71\u97ff\u3092\u53d7\u3051\u305a\u306b\u6027\u8cea\u306e\u3088\u3044\u95a2\u6570\u306e\u3068\u304d\u3068\u307b\u307c\u540c\u3058\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u305f. \u3053\u306e\u3088\u3046\u306b, \u7aef\u70b9\u306b\u7279\u7570\u70b9\u304c\u3042\u308b (\u7aef\u70b9\u3067\u5fae\u5206\u4fc2\u6570\u304c\u5b9a\u7fa9\u3067\u304d\u306a\u3044) \u5834\u5408\u306b\u3082\u9069\u7528\u3067\u304d\u308b\u3053\u3068\u306f IMT \u516c\u5f0f\u3068 DE \u516c\u5f0f\u306e\u7279\u9577\u306e\u3072\u3068\u3064\u3067\u3042\u308b.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (11) \u30d5\u30fc\u30ea\u30a8\u578b\u7a4d\u5206<\/h4>\n

\u6b21\u306e\u30d5\u30fc\u30ea\u30a8\u578b\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b.
\n\\[
\nI = \\int_0^{\\infty} log(x)sin(x) dx = -\\gamma
\n\\]\n

\"\"<\/p>\n

\u3053\u3053\u3067\u306f\u6587\u732e[7]\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u305f (\\(K = 2\\pi\\)). \u8981\u6c42\u7cbe\u5ea6 Tol \u3092\u9069\u5f53\u306b\u5909\u5316\u3055\u305b, \\(M = -\\pi log(Tol)\/2\\) \u3068\u56fa\u5b9a\u3057\u3066\u8a08\u7b97\u3057\u305f. \u3061\u306a\u307f\u306b, XLPack \u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b Deoint \u3067\u306f\u63a8\u5b9a\u8aa4\u5dee\u3092\u307f\u3066 M \u306e\u5024\u3092\u8abf\u7bc0\u3059\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n

9.2.3 \u8aa4\u5dee\u306e\u63a8\u5b9a<\/h3>\n

\u300c9.1.3 \u6570\u5024\u5b9f\u9a13\u300d\u3067\u898b\u305f\u3088\u3046\u306b\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u304c\u540c\u7a0b\u5ea6\u3067\u3042\u308c\u3070\u7a2e\u3005\u306e\u516c\u5f0f\u306e\u4e2d\u3067\u30ac\u30a6\u30b9\u516c\u5f0f\u304c\u6700\u3082\u7cbe\u5ea6\u304c\u826f\u304b\u3063\u305f. \u5358\u306b\u8a08\u7b97\u3059\u308b\u306e\u3067\u3042\u308c\u3070\u3053\u308c\u3067\u826f\u3044\u304c, \u5b9f\u52d9\u7684\u306b\u306f\u7a4d\u5206\u5024\u3068\u540c\u6642\u306b\u63a8\u5b9a\u8aa4\u5dee\u3082\u77e5\u308a\u305f\u3044. \u307e\u305f, \u5f8c\u3067\u793a\u3059\u81ea\u52d5\u7a4d\u5206\u306e\u30d9\u30fc\u30b9\u3068\u3057\u3066\u4f7f\u3046\u5834\u5408\u306b\u306f\u8aa4\u5dee\u63a8\u5b9a\u304c\u3067\u304d\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044. \u30ac\u30a6\u30b9\u516c\u5f0f\u306e\u5f31\u70b9\u306f\u8aa4\u5dee\u306e\u63a8\u5b9a\u304c\u3057\u306b\u304f\u3044\u3053\u3068\u3067\u3042\u308b.<\/p>\n

9.2.3.1 \u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u63a8\u5b9a<\/h3>\n

\u53f0\u5f62\u5247\u306e\u8a08\u7b97\u7d50\u679c\u306e\u8aa4\u5dee\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u306f, \u4f8b\u3048\u3070, N \u5206\u70b9\u3067\u8a08\u7b97\u3057\u305f\u3082\u306e\u3068 2N \u5206\u70b9\u3067\u8a08\u7b97\u3057\u305f\u3082\u306e\u3092\u6bd4\u8f03\u3059\u308b\u306a\u3069\u3059\u308c\u3070\u3088\u3044. \u6b21\u306e\u4f8b (\u6ed1\u3089\u304b\u306a\u95a2\u6570) \u3067\u53f0\u5f62\u5247\u306e\u8a08\u7b97\u4f8b\u3092\u898b\u308b.
\n\\[
\nI = \\int_0^1 e^x cos x dx = 1.37802461354736
\n\\]\n

\n\n\n\n\n\n\n\n
\u5206\u70b9\u6570<\/th>\n\u7a4d\u5206\u5024(\u8a08\u7b97\u5024)<\/th>\n\u7a4d\u5206\u5024(\u771f\u5024)<\/th>\n\u8aa4\u5dee<\/th>\n\u8aa4\u5dee\u63a8\u5b9a\u5024<\/th>\n<\/tr>\n
2<\/td>\n1.34061800327106<\/td>\n1.37802461354736<\/td>\n0.037406610<\/td>\n0.035423678<\/td>\n<\/tr>\n
4<\/td>\n1.36858238253106<\/td>\n1.37802461354736<\/td>\n0.009442231<\/td>\n0.009321460<\/td>\n<\/tr>\n
8<\/td>\n1.37565843490021<\/td>\n1.37802461354736<\/td>\n0.002366179<\/td>\n0.002358684<\/td>\n<\/tr>\n
16<\/td>\n1.37743271822098<\/td>\n1.37802461354736<\/td>\n0.000591895<\/td>\n0.000591428<\/td>\n<\/tr>\n
32<\/td>\n1.37787661780930<\/td>\n1.37802461354736<\/td>\n0.000147996<\/td>\n0.000147967<\/td>\n<\/tr>\n<\/table>\n<\/div>\n\u8aa4\u5dee\u63a8\u5b9a\u5024\u306f\u30ed\u30f3\u30d0\u30fc\u30b0\u7a4d\u5206\u306e\u6642\u3068\u540c\u3058\u3088\u3046\u306b\u6b21\u306e\u5f0f\u304b\u3089\u8a08\u7b97\u3057\u305f. \u5b9f\u969b\u306e\u8aa4\u5dee\u3068\u63a8\u5b9a\u5024\u306f\u3088\u304f\u4e00\u81f4\u3057\u3066\u3044\u308b.
\n\\[
\n\u63a8\u5b9a\u8aa4\u5dee = \\frac{4I – I_{prev}}{3}
\n\\]\n\u3053\u3053\u3067\u306f\u5206\u70b9\u6570\u3092\u500d\u3005\u306b\u3059\u308b\u3088\u3046\u306a\u9806\u5e8f (\u7b49\u9593\u9694\u306a\u5206\u5272\u5e45\u305d\u308c\u305e\u308c\u3092\u534a\u5206\u306b\u3057\u3066\u3044\u304f) \u3067\u8a08\u7b97\u3092\u884c\u3063\u305f. \\(I\\) \u306f\u7a4d\u5206\u306e\u8a08\u7b97\u5024, \\(I_{prev}\\) \u306f\u5206\u70b9\u6570\u304c\u534a\u5206\u306e\u6642\u306e (\u3064\u307e\u308a 1 \u3064\u524d\u306e) \u8a08\u7b97\u5024\u3067\u3042\u308b. \u3053\u306e\u5834\u5408, \u5206\u70b9\u6570\u3092\u500d\u306b\u3057\u305f\u6642\u306b\u3082\u3046\u4e00\u56de\u6700\u521d\u304b\u3089\u5168\u90e8\u306e\u5206\u70b9\u3067\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u306f\u306a\u304f, \u534a\u5206\u306f\u3059\u3067\u306b\u8a08\u7b97\u6e08\u306e\u5024\u304c\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b.<\/p>\n

9.2.3.2 \u8aa4\u5dee\u63a8\u5b9a\u6a5f\u80fd\u4ed8\u304d\u306e\u30ac\u30a6\u30b9\u516c\u5f0f<\/h3>\n

\u53f0\u5f62\u5247\u3068\u306f\u7570\u306a\u308a, \u30ac\u30a6\u30b9\u516c\u5f0f\u3067\u306f\u5206\u70b9\u304c\u7b49\u9593\u9694\u3067\u306a\u3044\u305f\u3081, \u5206\u70b9\u6570\u3092\u500d\u306b\u3059\u308b\u3068\u3082\u3046\u4e00\u56de\u6700\u521d\u304b\u3089\u5168\u90e8\u306e\u5206\u70b9\u3067\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u306e\u304c\u5f31\u70b9\u3067\u3042\u308b.<\/p>\n

\u3053\u308c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b, N \u70b9\u30ac\u30a6\u30b9\u516c\u5f0f\u306e\u8a08\u7b97\u5024\u3092\u751f\u304b\u3057\u305f\u307e\u307e 2N + 1 \u70b9\u3092\u4f7f\u3063\u305f\u7a4d\u5206\u516c\u5f0f\u304c\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f<\/strong>\u3067\u3042\u308b.<\/p>\n

N \u70b9\u30ac\u30a6\u30b9\u516c\u5f0f\u306b\u3088\u308b\u7a4d\u5206\u3092 \\(G_N\\) \u3067\u8868\u3059 (\u7a4d\u5206\u533a\u9593\u3092 [-1, 1] \u3068\u3059\u308b).
\n\\[
\nG_N = \\sum_{i=1}^N w_i f(x_i)
\n\\]\n\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u3067\u306f\u540c\u3058 N \u500b\u306e\u5206\u70b9 \\(x_i\\) \u3068\u65b0\u305f\u306b\u8a08\u7b97\u304c\u5fc5\u8981\u306a N + 1 \u500b\u306e\u5206\u70b9 \\(y_i\\) \u3092\u4f7f\u3063\u3066\u6c42\u3081\u308b\u7a4d\u5206 \\(K_{2N+1}\\) \u3092\u6b21\u5f0f\u3067\u8868\u3059.
\n\\[
\nK_{2N+1} = \\sum_{i=1}^N a_i f(x_i) + \\sum_{j=1}^{N+1} b_j f(y_j)
\n\\]\nN \u500b\u306e\u5206\u70b9 \\(x_i\\) \u306b\u304a\u3051\u308b\u4fc2\u6570 \\(a_i\\) \u306f\u30ac\u30a6\u30b9\u516c\u5f0f\u306e\u4fc2\u6570 \\(w_i\\) \u3068\u306f\u7570\u306a\u308b\u5024\u306b\u306a\u308b.<\/p>\n

N \u70b9\u30ac\u30a6\u30b9\u516c\u5f0f \\(G_N\\) \u306f 2N – 1 \u6b21\u591a\u9805\u5f0f\u307e\u3067\u6b63\u3057\u3044\u89e3\u3092\u4e0e\u3048\u308b (\u3059\u306a\u308f\u3061 2N – 1 \u6b21\u3067\u3042\u308b) \u304c, \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f \\(K_{2N+1}\\) \u306f 3N + 1 \u6b21 (N \u304c\u5076\u6570\u306e\u3068\u304d\u306f 3N + 2 \u6b21) \u3068\u306a\u308b\u3088\u3046\u306b\u5206\u70b9\u3068\u91cd\u307f\u3092\u9078\u3076.<\/p>\n

\\(x_i\\) \u306f N \u6b21\u306e\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u591a\u9805\u5f0f \\(P_N(x)\\) \u306e\u30bc\u30ed\u70b9\u3067\u3042\u308b\u304c, \u6b8b\u308a\u306e\u5206\u70b9 \\(y_i\\) \u304c n + 1 \u6b21\u306e\u591a\u9805\u5f0f \\(E_{N+1}(x)\\) \u306e\u30bc\u30ed\u70b9\u306b\u306a\u308b\u3068\u3059\u308b\u3068, \\(E_{N+1}(x)\\) \u306f\u6b21\u306e\u76f4\u4ea4\u95a2\u4fc2\u3092\u6e80\u305f\u3059.
\n\\[
\n\\int P_N(x) E_{N+1}(x) x^k dx = 0 \\space (k = 0, \\dots, N)
\n\\]\n\u4e0a\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u591a\u9805\u5f0f \\(E_{N+1}(x)\\) \u306e\u30bc\u30ed\u70b9\u306f\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d, \u533a\u9593 (-1, 1) \u306b\u5b58\u5728\u3057, \\(P_N(x)\\) \u306e\u30bc\u30ed\u70b9\u3068\u4ea4\u4e92\u306b\u73fe\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b. \u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u306f\u3053\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u6c42\u3081\u305f\u304c, \u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u975e\u5e38\u306b\u60aa\u6761\u4ef6\u3067\u89e3\u304d\u306b\u304f\u3044\u305f\u3081, \u5f8c\u306b\u3044\u304f\u3064\u304b\u306e\u8a08\u7b97\u6cd5\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u308b.<\/p>\n

N = 2 \uff5e 10 \u306e\u3068\u304d\u306e\u5206\u70b9\u304a\u3088\u3073\u91cd\u307f\u306e\u5024\u3092\u300c9.2.5 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868\u300d\u306b\u63b2\u8f09\u3057\u305f. \u3053\u3053\u3067\u306f, \u6587\u732e[8]\u306b\u5f93\u3044, \u30e4\u30b3\u30d3\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u884c\u5217\u3068\u3088\u3070\u308c\u308b\u5bfe\u79f0\u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u3092\u4f5c\u308a\u305d\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306b\u3088\u308a\u8a08\u7b97\u3057\u305f.<\/p>\n

\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u3067\u306f, 2N + 1 \u56de\u306e\u95a2\u6570\u8a55\u4fa1\u3067 2N + 1 \u6b21\u306e \\(G_N\\) \u3068 \\(3N + 1\\) \u6b21\u306e \\(K_{2N+1}\\) \u306e\u4e21\u65b9\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d, \u3053\u306e 2 \u3064\u3092\u6bd4\u3079\u308b\u3053\u3068\u306b\u3088\u308a\u8aa4\u5dee\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b. \u63a8\u5b9a\u8aa4\u5dee\u306f\u7d4c\u9a13\u7684\u306b\u6b21\u5f0f\u3067\u8868\u3055\u308c\u308b.
\n\\[
\n\u63a8\u5b9a\u8aa4\u5dee = (200*|G_N – K_{2N+1}|)^{1.5}
\n\\]\n\u3053\u306e\u5f0f\u306b\u3088\u308b\u63a8\u5b9a\u8aa4\u5dee\u306f\u5b89\u5168\u5074\u306b\u6c42\u3081\u3089\u308c\u308b\u3068\u3055\u308c\u3066\u3044\u308b.<\/p>\n

\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f \\(K_{2N+1}\\) \u306f 3N + 1 \u6b21\u3067\u3042\u308b\u304c, \u540c\u3058\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u8a08\u7b97\u3067\u304d\u308b\u30ac\u30a6\u30b9\u516c\u5f0f \\(G_{2N+1}\\) \u306f 4N + 1 \u6b21\u3067\u3042\u308b. \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u306f\u7cbe\u5ea6\u7684\u306b\u306f\u30ac\u30a6\u30b9\u516c\u5f0f\u306b\u52a3\u308b\u304c, \u8aa4\u5dee\u306e\u63a8\u5b9a\u304c\u3067\u304d\u308b\u5229\u70b9\u306e\u65b9\u304c\u5927\u304d\u3044\u5834\u5408\u306b\u6709\u52b9\u3067\u3042\u308b.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (12) \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f<\/h4>\n

\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u3092\u7528\u3044\u3066\u6b21\u306e\u7a4d\u5206\u3092\u6c42\u3081\u308b.
\n\\[
\nI = \\int_0^1 e^x cos(x) dx = 1.37802461354736
\n\\]\n\u3053\u308c\u306f\u524d\u306b\u3082\u4f8b\u984c\u306b\u4f7f\u7528\u3057\u305f\u6027\u8cea\u306e\u3088\u3044\u95a2\u6570\u3067\u3042\u308a, \u8a08\u7b97\u7d50\u679c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n

\"\"<\/p>\n

\u6a2a\u8ef8\u306b\u95a2\u6570\u8a55\u4fa1\u56de\u6570, \u7e26\u8ef8\u306b\u8aa4\u5dee\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u305f. \u7dd1\u8272\u306e\u30c7\u30fc\u30bf\u306f\u524d\u9805\u306e\u5f0f\u3067\u6c42\u3081\u305f\u63a8\u5b9a\u8aa4\u5dee\u3067\u3042\u308b. \u6a2a\u8ef8\u306f\u5206\u70b9\u6570 (\u30ac\u30a6\u30b9\u516c\u5f0f\u3067\u306f N, \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u3067\u306f 2N + 1 \u306e\u5024) \u306b\u7b49\u3057\u3044.<\/p>\n

\u63a8\u5b9a\u8aa4\u5dee\u306f\u304b\u306a\u308a\u5b89\u5168\u5074\u306b\u7b97\u51fa\u3055\u308c\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b.<\/p>\n

\u6570\u5024\u5b9f\u9a13 (13) \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f (\u7279\u7570\u6027\u306e\u3042\u308b\u5834\u5408)<\/h4>\n

\u4e0a\u306e\u4f8b\u984c\u3067\u306f\u53ce\u675f\u304c\u901f\u304f\u3059\u3050\u306b\u4e38\u3081\u8aa4\u5dee\u306e\u9818\u57df\u306b\u5165\u3063\u3066\u3044\u3066\u3046\u307e\u304f\u6bd4\u8f03\u3067\u304d\u306a\u3044\u306e\u3067\u3082\u3046\u5c11\u3057\u96e3\u3057\u3044\u6b21\u306e\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b.
\n\\[
\nI = \\int_0^4 1\/(1 + x)dx = ln(1 + 4) = ln(5)
\n\\]\n\u3053\u308c\u3082\u524d\u306b\u4f8b\u984c\u306b\u4f7f\u7528\u3057\u305f\u95a2\u6570\u3067, \u7a4d\u5206\u533a\u9593\u5916\u3067\u3042\u308b\u304c\u8fd1\u304f\u306b\u7279\u7570\u70b9\u3092\u6301\u3064.<\/p>\n

\"\"<\/p>\n

\u3053\u306e\u4f8b\u3067\u306f\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u3082\u305d\u308c\u307b\u3069\u5927\u304d\u306a\u30da\u30ca\u30eb\u30c6\u30a3\u3092\u6255\u308f\u305a\u306b\u8aa4\u5dee\u3092\u63a8\u5b9a\u3067\u304d\u3066\u3044\u308b.<\/p>\n

9.2.4 \u81ea\u52d5\u7a4d\u5206\u30d7\u30ed\u30b0\u30e9\u30e0<\/h3>\n

\u81ea\u52d5\u7a4d\u5206\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u306f, \u7a4d\u5206\u533a\u9593\u3068\u8981\u6c42\u7cbe\u5ea6\u3092\u4e0e\u3048\u308b\u3068\u8aa4\u5dee\u63a8\u5b9a\u5024\u304c\u8981\u6c42\u7cbe\u5ea6\u3092\u6e80\u305f\u3059\u307e\u3067\u304d\u3056\u307f\u5e45\u3092\u9806\u6b21\u5c0f\u3055\u304f\u3059\u308b\u306a\u3069\u3057\u3066\u7a4d\u5206\u3092\u7e70\u308a\u8fd4\u3059\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u3042\u308b.<\/p>\n

\u9069\u5fdc\u81ea\u52d5\u7a4d\u5206\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3053\u308c\u3092\u4e00\u6b69\u9032\u3081\u3066, \u7a4d\u5206\u533a\u9593\u3092\u90e8\u5206\u533a\u9593\u306b\u5206\u5272\u3057, \u8aa4\u5dee\u63a8\u5b9a\u5024\u304c\u8981\u6c42\u3055\u308c\u305f\u7cbe\u5ea6\u3092\u6e80\u305f\u3059\u3088\u3046\u306b\u90e8\u5206\u533a\u9593\u306e\u5e45\u3092\u81ea\u52d5\u7684\u306b\u8abf\u7bc0\u3059\u308b\u3082\u306e\u3067\u3042\u308b. \u88ab\u7a4d\u5206\u95a2\u6570\u304c\u306a\u3081\u3089\u304b\u306b\u3086\u3063\u304f\u308a\u5909\u5316\u3059\u308b\u3088\u3046\u306a\u533a\u9593\u3067\u306f\u5927\u304d\u306a\u533a\u9593\u5e45\u3092\u7528\u3044, \u8aa4\u5dee\u63a8\u5b9a\u5024\u304c\u5927\u304d\u3044\u90e8\u5206\u3067\u306f\u7d30\u304b\u3044\u533a\u9593\u306b\u5206\u5272\u3057\u3066\u304d\u3056\u307f\u5e45\u3092\u5c0f\u3055\u304f\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u308a, \u6700\u5c0f\u306e\u8a08\u7b97\u91cf\u3067\u8981\u6c42\u7cbe\u5ea6\u306e\u7d50\u679c\u3092\u5f97\u3088\u3046\u3068\u3059\u308b\u3082\u306e\u3067\u3042\u308b.<\/p>\n

\u9069\u5fdc\u81ea\u52d5\u7a4d\u5206\u3068\u3057\u3066\u306f, \u8aa4\u5dee\u63a8\u5b9a\u3092\u884c\u3046\u305f\u3081\u3068\u8a08\u7b97\u6e08\u306e\u95a2\u6570\u5024\u3092\u518d\u5229\u7528\u3059\u308b\u305f\u3081\u306b, \u5206\u70b9\u304c\u7b49\u9593\u9694\u306a\u30b7\u30f3\u30d7\u30bd\u30f3\u5247\u3084\u30cb\u30e5\u30fc\u30c8\u30f3\u30fb\u30b3\u30fc\u30c4\u516c\u5f0f\u304c\u4f7f\u308f\u308c\u3066\u304d\u305f. \u3057\u304b\u3057, \u73fe\u5728\u3067\u306f\u7cbe\u5ea6\u3092\u8ffd\u6c42\u3057\u3066, \u8aa4\u5dee\u63a8\u5b9a\u6a5f\u80fd\u3092\u6301\u3064\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u306e\u3088\u3046\u306a\u4e0d\u7b49\u9593\u9694\u5206\u70b9\u3067\u306f\u3042\u308b\u304c\u9ad8\u7cbe\u5ea6\u306e\u516c\u5f0f\u3092\u4f7f\u3063\u305f\u3082\u306e\u304c\u4f7f\u308f\u308c\u3066\u3044\u308b.<\/p>\n

9.2.4.1 \u9069\u5fdc\u81ea\u52d5\u7a4d\u5206\u30d7\u30ed\u30b0\u30e9\u30e0 QAG<\/h3>\n

\u9069\u5fdc\u81ea\u52d5\u7a4d\u5206\u30eb\u30fc\u30c1\u30f3\u306e\u4f8b\u3068\u3057\u3066 QUADPACK (\u6587\u732e[6]) \u306e QAG \u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u8aac\u660e\u3059\u308b. QAG \u306f\u8981\u6c42\u7cbe\u5ea6\u3092\u6e80\u305f\u3059\u307e\u3067\u81ea\u52d5\u7684\u306b\u7a4d\u5206\u533a\u9593\u3092\u90e8\u5206\u533a\u9593\u306b\u5206\u5272\u3057\u306a\u304c\u3089\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u306e\u56fa\u5b9a\u5206\u70b9\u30d7\u30ed\u30b0\u30e9\u30e0 (QK15, …, QK61) \u3092\u547c\u3073\u51fa\u3059\u3053\u3068\u306b\u3088\u308a\u81ea\u52d5\u7a4d\u5206\u3092\u884c\u3046. XLPack \u306b\u306f Qag \u3068\u3057\u3066\u53ce\u9332\u3055\u308c\u3066\u304a\u308a, \u901a\u5e38\u306e\u6570\u5024\u7a4d\u5206\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066\u306f\u6700\u3082\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u308b.<\/p>\n

\u3053\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u52d5\u4f5c\u306e\u6982\u8981\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n

\u4e0e\u3048\u3089\u308c\u305f\u53ce\u675f\u6761\u4ef6\u3092\u300c\u63a8\u5b9a\u8aa4\u5dee \\(\\le\\) Tol\u300d\u3068\u3059\u308b.<\/p>\n

    \n
  1. \u307e\u305a, \u5168\u533a\u9593\u3092\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u306e\u56fa\u5b9a\u5206\u70b9\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u308a\u7a4d\u5206\u3092\u884c\u3044\u7a4d\u5206\u5024 S \u3068\u63a8\u5b9a\u8aa4\u5dee E \u3092\u6c42\u3081\u308b.<\/li>\n
  2. E \\(>\\) Tol \u3067\u3042\u308b\u9650\u308a\u4ee5\u4e0b\u3092\u7e70\u308a\u8fd4\u3059.\n
      \n
    1. \u63a8\u5b9a\u8aa4\u5dee\u304c\u6700\u3082\u5927\u304d\u3044\u90e8\u5206\u533a\u9593\u3092\u534a\u5206\u306b\u5206\u5272\u3057\u3066\u305d\u308c\u305e\u308c\u3092\u56fa\u5b9a\u5206\u70b9\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u308a\u7a4d\u5206\u3057, \u7a4d\u5206\u5024 \\(S_i\\) \u3068\u63a8\u5b9a\u8aa4\u5dee \\(E_i\\) \u3092\u6c42\u3081\u308b(i \u306f\u90e8\u5206\u533a\u9593\u3054\u3068\u306e\u5024\u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3059).<\/li>\n
    2. \u65b0\u305f\u306b\u69cb\u6210\u3055\u308c\u305f\u3082\u306e\u3092\u542b\u3081\u305f\u3059\u3079\u3066\u306e\u90e8\u5206\u533a\u9593\u306b\u304a\u3051\u308b\u7a4d\u5206\u5024\u3068\u63a8\u5b9a\u8aa4\u5dee\u306e\u305d\u308c\u305e\u308c\u306e\u7dcf\u548c S \u3068 E \u3092\u66f4\u65b0\u3059\u308b.<\/li>\n<\/ol>\n<\/li>\n
    3. E \\(\\le\\) Tol \u306b\u306a\u3063\u305f\u3089\u305d\u306e\u6642\u306e\u7a4d\u5206\u5024\u306e\u7dcf\u548c S \u3092\u6700\u7d42\u7d50\u679c\u3068\u3057\u3066\u8fd4\u3059.<\/li>\n<\/ol>\n

      QAG \u3067\u306f\u30d9\u30fc\u30b9\u306e\u56fa\u5b9a\u5206\u70b9\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066 QK15, …, QK61 \u306e\u3046\u3061\u30e6\u30fc\u30b6\u30fc\u304c\u6307\u5b9a\u3057\u305f\u3082\u306e\u3092\u4f7f\u7528\u3057, \u3053\u308c\u3092\u81ea\u52d5\u7684\u306b\u5909\u66f4\u3059\u308b\u3053\u3068\u306f\u3057\u306a\u3044. \u307e\u305f, \u533a\u9593\u3092\u5206\u5272\u3059\u308b\u969b\u306b\u8a08\u7b97\u6e08\u306e\u95a2\u6570\u5024\u3092\u518d\u5229\u7528\u3059\u308b\u3053\u3068\u3082\u3057\u306a\u3044.<\/p>\n

      \u6570\u5024\u5b9f\u9a13 (14) Qag (Qk15)<\/h4>\n

      \u4f8b\u3068\u3057\u3066, \u533a\u9593 [0,1] \u306b\u304a\u3044\u3066\u6b21\u306e\u95a2\u6570 (\u6587\u732e[1]\u53c2\u7167) \u3092\u7a4d\u5206\u3057\u305f\u6642\u306e QAG \u306e\u6319\u52d5\u3092\u4e0b\u56f3\u306b\u793a\u3059.
      \n\\[
      \nf(x) = \\frac{1}{(x – 0.3)^2 + 0.01} + \\frac{1}{(x – 0.9)^2 + 0.04} – 6
      \n\\]\n

      \"\"<\/p>\n

      \u3053\u3053\u3067\u306f, XLPack \u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b Qag \u3092\u4f7f\u7528\u3057, \u76ee\u7684\u8aa4\u5dee\u3092 \\(10^{-5}\\) \u3068\u3057\u3066\u56fa\u5b9a\u5206\u70b9\u30d7\u30ed\u30b0\u30e9\u30e0\u306f Qk15 \u3092\u6307\u5b9a\u3057\u3066\u8a08\u7b97\u3057\u305f. \u533a\u9593\u306f 5 \u3064\u306b\u5206\u5272\u3055\u308c\u305f (0 \uff5e 0.25, 0.25 \uff5e 0.375, 0.375 \uff5e 0.5, 0.5 \uff5e 0.75, 0.75 \uff5e 1). \u30c8\u30fc\u30bf\u30eb\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u306f 135 \u56de\u3067\u3042\u3063\u305f. \u6700\u3082\u6025\u5cfb\u306a\u5909\u5316\u306e\u3068\u3053\u308d\u3067\u5206\u5272\u3055\u308c\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b.<\/p>\n

      \u6570\u5024\u5b9f\u9a13 (15) Qag (Qk61)<\/h4>\n

      \u540c\u3058\u6761\u4ef6\u3067 Qk61 \u3092\u6307\u5b9a\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n

      \"\"<\/p>\n

      2 \u5206\u5272\u3067\u8a08\u7b97\u3057\u3066\u304a\u308a (0 \uff5e 0.5, 0.5 \uff5e 1), \u30c8\u30fc\u30bf\u30eb\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u306f 183 \u56de\u306b\u306a\u3063\u305f. \u5909\u5316\u304c\u6fc0\u3057\u3044\u5834\u5408\u306b\u306f QK15 \u3092\u9078\u629e\u3057\u5206\u5272\u6570\u3092\u591a\u304f\u3057, \u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306b\u306f QK61 \u306e\u3088\u3046\u306b\u9ad8\u7cbe\u5ea6\u306e\u3082\u306e\u3092\u9078\u3073\u5206\u5272\u6570\u3092\u5c11\u306a\u304f\u3059\u308b\u3068\u3088\u3055\u305d\u3046\u3067\u3042\u308b.<\/p>\n

      9.2.5 \u7a4d\u5206\u516c\u5f0f\u306e\u4fc2\u6570\u8868<\/h3>\n

      (1) \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f<\/h3>\n

      \\[
      \nK_{2N+1} = \\sum_{i=1}^N a_i f(x_i) + \\sum_{j=1}^{n+1} b_j f(y_j)
      \n\\]\n\u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u306b\u304a\u3051\u308b\u5206\u70b9 \\(x_i, y_j \u304a\u3088\u3073\u91cd\u307f a_i, b_j\\) \u3092\u4ee5\u4e0b\u306b\u793a\u3059(\\(x_i\\) \u306f\u30ac\u30a6\u30b9\u516c\u5f0f\u306e \\(x_i\\) \u3068\u540c\u3058). \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

      N \u306f\u5bfe\u5fdc\u3059\u308b\u30ac\u30a6\u30b9\u516c\u5f0f\u306e N \u306e\u5024\u3092\u793a\u3059. \u30ac\u30a6\u30b9\u30fb\u30af\u30ed\u30f3\u30ed\u30c3\u30c9\u516c\u5f0f\u3068\u3057\u3066\u306e\u5206\u70b9\u6570\u306f 2N + 1 \u3068\u306a\u308b (\u4f8b. N = 7 \u306f 15 \u5206\u70b9).<\/p>\n

        \r\nN = 2\r\n  xi: -5.773502691896258E-0001  5.773502691896258E-0001\r\n  ai:  4.909090909090909E-0001  4.909090909090909E-0001\r\n  yi: -9.258200997725515E-0001  0.000000000000000E+0000  9.258200997725515E-0001\r\n  bi:  1.979797979797980E-0001  6.222222222222222E-0001  1.979797979797980E-0001\r\nN = 3\r\n  xi: -7.745966692414834E-0001  0.000000000000000E+0000  7.745966692414834E-0001\r\n  ai:  2.684880898683334E-0001  4.509165386584741E-0001  2.684880898683334E-0001\r\n  yi: -9.604912687080203E-0001 -4.342437493468026E-0001  4.342437493468026E-0001\r\n       9.604912687080203E-0001\r\n  bi:  1.046562260264673E-0001  4.013974147759622E-0001  4.013974147759622E-0001\r\n       1.046562260264673E-0001\r\nN = 4\r\n  xi: -8.611363115940526E-0001 -3.399810435848563E-0001  3.399810435848563E-0001\r\n       8.611363115940526E-0001\r\n  ai:  1.700536053357227E-0001  3.269491896014516E-0001  3.269491896014516E-0001\r\n       1.700536053357227E-0001\r\n  yi: -9.765602507375731E-0001 -6.402862174963100E-0001  0.000000000000000E+0000\r\n       6.402862174963100E-0001  9.765602507375731E-0001\r\n  bi:  6.297737366547301E-0002  2.667983404522844E-0001  3.464429818901364E-0001\r\n       2.667983404522844E-0001  6.297737366547301E-0002\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  ai:  1.152333166224734E-0001  2.410403392286476E-0001  2.829874178574912E-0001\r\n       2.410403392286476E-0001  1.152333166224734E-0001\r\n  yi: -9.840853600948425E-0001 -7.541667265708492E-0001 -2.796304131617832E-0001\r\n       2.796304131617832E-0001  7.541667265708492E-0001  9.840853600948425E-0001\r\n  bi:  4.258203675108183E-0002  1.868007965564927E-0001  2.728498019125589E-0001\r\n       2.728498019125589E-0001  1.868007965564927E-0001  4.258203675108183E-0002\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  ai:  8.369444044690663E-0002  1.810719943231376E-0001  2.337708641169944E-0001\r\n       2.337708641169944E-0001  1.810719943231376E-0001  8.369444044690663E-0002\r\n  yi: -9.887032026126789E-0001 -8.213733408650279E-0001 -4.631182124753046E-0001\r\n       0.000000000000000E+0000  4.631182124753046E-0001  8.213733408650279E-0001\r\n       9.887032026126789E-0001\r\n  bi:  3.039615411981977E-0002  1.373206046344469E-0001  2.132096522719623E-0001\r\n       2.410725801734648E-0001  2.132096522719623E-0001  1.373206046344469E-0001\r\n       3.039615411981977E-0002\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  ai:  6.309209262997855E-0002  1.406532597155259E-0001  1.903505780647854E-0001\r\n       2.094821410847278E-0001  1.903505780647854E-0001  1.406532597155259E-0001\r\n       6.309209262997855E-0002\r\n  yi: -9.914553711208126E-0001 -8.648644233597691E-0001 -5.860872354676911E-0001\r\n      -2.077849550078985E-0001  2.077849550078985E-0001  5.860872354676911E-0001\r\n       8.648644233597691E-0001  9.914553711208126E-0001\r\n  bi:  2.293532201052922E-0002  1.047900103222502E-0001  1.690047266392679E-0001\r\n       2.044329400752989E-0001  2.044329400752989E-0001  1.690047266392679E-0001\r\n       1.047900103222502E-0001  2.293532201052923E-0002\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  ai:  4.943939500213931E-0002  1.116463708268396E-0001  1.566526061681884E-0001\r\n       1.814000250680346E-0001  1.814000250680346E-0001  1.566526061681884E-0001\r\n       1.116463708268396E-0001  4.943939500213931E-0002\r\n  yi: -9.933798758817162E-0001 -8.941209068474564E-0001 -6.723540709451587E-0001\r\n      -3.607010979281320E-0001  0.000000000000000E+0000  3.607010979281320E-0001\r\n       6.723540709451587E-0001  8.941209068474564E-0001  9.933798758817162E-0001\r\n  bi:  1.782238332071036E-0002  8.248229893135833E-0002  1.362631092551722E-0001\r\n       1.720706085552113E-0001  1.844464057446916E-0001  1.720706085552113E-0001\r\n       1.362631092551722E-0001  8.248229893135833E-0002  1.782238332071036E-0002\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  ai:  3.963189516026125E-0002  9.079068168872639E-0002  1.300014068553412E-0001\r\n       1.564135277884839E-0001  1.648960128283494E-0001  1.564135277884839E-0001\r\n       1.300014068553412E-0001  9.079068168872639E-0002  3.963189516026126E-0002\r\n  yi: -9.946781606773402E-0001 -9.149635072496779E-0001 -7.344867651839338E-0001\r\n      -4.754624791124599E-0001 -1.642235636149868E-0001  1.642235636149868E-0001\r\n       4.754624791124599E-0001  7.344867651839338E-0001  9.149635072496779E-0001\r\n       9.946781606773402E-0001\r\n  bi:  1.430477564383894E-0002  6.651815594027414E-0002  1.117891346844183E-0001\r\n       1.452395883843662E-0001  1.628628274401151E-0001  1.628628274401151E-0001\r\n       1.452395883843662E-0001  1.117891346844183E-0001  6.651815594027414E-0002\r\n       1.430477564383894E-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  ai:  3.255816230796473E-0002  7.503967481091995E-0002  1.093871588022976E-0001\r\n       1.347092173114733E-0001  1.477391049013385E-0001  1.477391049013385E-0001\r\n       1.347092173114733E-0001  1.093871588022976E-0001  7.503967481091995E-0002\r\n       3.255816230796473E-0002\r\n  yi: -9.956571630258081E-0001 -9.301574913557082E-0001 -7.808177265864169E-0001\r\n      -5.627571346686047E-0001 -2.943928627014602E-0001  0.000000000000000E+0000\r\n       2.943928627014602E-0001  5.627571346686047E-0001  7.808177265864169E-0001\r\n       9.301574913557082E-0001  9.956571630258081E-0001\r\n  bi:  1.169463886737187E-0002  5.475589657435200E-0002  9.312545458369761E-0002\r\n       1.234919762620659E-0001  1.427759385770601E-0001  1.494455540029169E-0001\r\n       1.427759385770601E-0001  1.234919762620659E-0001  9.312545458369761E-0002\r\n       5.475589657435200E-0002  1.169463886737187E-0002\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
      9.2.1 \u53f0\u5f62\u5247\u306e\u8aa4\u5dee \u53f0\u5f62\u5247\u3067\u306f\u5206\u70b9\u6570\u3092\u500d (\u523b\u307f\u5e45 h \u3092 1\/2) \u306b\u3059\u308b\u3068\u8aa4\u5dee\u306f\u304a\u304a\u3088\u305d 1\/4 \u306b\u306a\u3063\u305f. \u3053\u308c\u306f, \u88ab\u7a4d\u5206\u95a2\u6570\u304c\u89e3\u6790\u7684\u306a\u5834\u5408\u53f0\u5f62\u5247\u306e\u8aa4\u5dee\u304c\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3053\u3068\u306b\u3088\u308b (\u30aa\u30a4\u30e9\u30fc\u30fb\u30de\u30af\u30ed\u30fc\u30ea […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-5899","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\t