{"id":5423,"date":"2026-05-26T10:22:55","date_gmt":"2026-05-26T01:22:55","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=5423"},"modified":"2026-05-26T10:22:55","modified_gmt":"2026-05-26T01:22:55","slug":"6-2_inter","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/6-2_inter\/","title":{"rendered":"6.2 \u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593"},"content":{"rendered":"\n\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u516c\u5f0f\u306f\u6a19\u672c\u70b9\u306b\u304a\u3044\u3066\u95a2\u6570\u5024\u304c\u4e00\u81f4\u3059\u308b\u8fd1\u4f3c\u5f0f\u3092\u4e0e\u3048\u305f. \u3053\u308c\u306b\u5bfe\u3057\u3066, \u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593\u306f\u3084\u306f\u308a\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u304c\u6a19\u672c\u70b9\u306b\u304a\u3044\u3066\u95a2\u6570\u5024\u306e\u4ed6\u306b\u5fae\u5206\u5024\u3082\u4e00\u81f4\u3059\u308b\u8fd1\u4f3c\u5f0f\u3092\u4e0e\u3048\u308b.<\/p>\n

6.2.1 \u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593<\/h3>\n

\u533a\u9593 \\([a, b]\\) \u5185\u306e n + 1 \u500b\u306e\u76f8\u7570\u306a\u308b\u70b9 \\(x_0, x_1, \\dots, x_n\\) \u306b\u304a\u3051\u308b\u95a2\u6570 \\(f(x)\\) \u306e\u5024 \\(f(x_0), f(x_1), \\dots, f(x_n)\\) \u304a\u3088\u3073\u5fae\u5206\u5024 \\(f'(x)\\) \u306e\u5024 \\(f'(x_0), f'(x_1), \\dots, f'(x_n)\\) \u304c\u30c7\u30fc\u30bf\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u3068\u304d, \u3053\u308c\u3089\u306e\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u5024\u304a\u3088\u3073\u5fae\u5206\u5024\u304c\u30c7\u30fc\u30bf\u306b\u4e00\u81f4\u3059\u308b\u3088\u3046\u306a\u8fd1\u4f3c\u5f0f\u3092\u8003\u3048\u308b.<\/p>\n

\u6761\u4ef6\u304c 2n + 2 \u500b\u3042\u308b\u306e\u3067, \u3053\u308c\u3092\u6e80\u8db3\u3059\u308b\u305f\u3081\u306b\u306f 2n + 2 \u500b\u306e\u4fc2\u6570\u304c\u3042\u308b 2n + 1 \u6b21\u591a\u9805\u5f0f \\(p_{2n+1}(x)\\) \u304c\u5fc5\u8981\u3067, \u6b21\u5f0f\u3092\u6e80\u305f\u3059.
\n\\[
\n\\begin{align}
\n& p_{2n+1}(x_k) = f(x_k) (k = 0 \\sim n) \\\\
\n& p_{2n+1}'(x_k) = f'(x_k) (k = 0 \\sim n) \\\\
\n\\end{align}
\n\\]\n\\(p_{2n+1}(x)\\) \u306e\u4fc2\u6570\u3092 \\(a_0, a_1, \\dots, a_{2n+1}\\) \u3068\u3059\u308b\u3068
\n\\[
\n\\begin{align}
\n& p_{2n+1}(x) = \\sum_{i=0}^{2n+1}a_ix^{2n+1-i} \\\\
\n& p_{2n+1}'(x) = \\sum_{i=0}^{2n+1}(2n+1-i)a_ix^{2n-i} \\\\
\n\\end{align}
\n\\]\n\u3067\u3042\u308b\u304b\u3089, \u6b21\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u308a\u8fd1\u4f3c\u591a\u9805\u5f0f\u306e\u4fc2\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.
\n\\[
\n\\boldsymbol{V}\\boldsymbol{a} = \\boldsymbol{f}
\n\\]\n\u305f\u3060\u3057,
\n\\[
\n\\boldsymbol{V} =
\n\\begin{pmatrix}
\nx_0^{2n+1} & x_0^{2n} & \\dots & x_0 & 1 \\\\
\n(2n+1)x_0^{2n} & (2n)x_0^{2n-1} & \\dots & 1 & 0 \\\\
\nx_1^{2n+1} & x_1^{2n} & \\dots & x_1 & 1 \\\\
\n(2n+1)x_1^{2n} & (2n)x_1^{2n-1} & \\dots & 1 & 0 \\\\
\n & \\vdots \\\\
\nx_n^{2n+1} & x_n^{2n} & \\dots & x_n & 1 \\\\
\n(2n+1)x_n^{2n} & (2n)x_n^{2n-1} & \\dots & 1 & 0 \\\\
\n\\end{pmatrix}
\n,
\n\\boldsymbol{a} =
\n\\begin{pmatrix}
\na_0 \\\\
\na_1 \\\\
\na_2 \\\\
\na_3 \\\\
\n\\vdots \\\\
\na_{2n} \\\\
\na_{2n+1} \\\\
\n\\end{pmatrix}
\n,
\n\\boldsymbol{f} =
\n\\begin{pmatrix}
\nf_0 \\\\
\nf’_0 \\\\
\nf_1 \\\\
\nf’_1 \\\\
\n\\vdots \\\\
\nf_n \\\\
\nf’_n \\\\
\n\\end{pmatrix}
\n\\]\n

\u3053\u3053\u3067, \\(\\boldsymbol{V}\\) \u306f\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u884c\u5217, \\(\\boldsymbol{f}\\) \u306f\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u30d9\u30af\u30c8\u30eb (\u5404\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u5024 \\(f_i = f(x_i)\\) \u304a\u3088\u3073\u5fae\u5206\u5024 \\(f’_i = f'(x_i)\\) \u3092\u8868\u3059), \\(\\boldsymbol{a}\\) \u306f\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u30d9\u30af\u30c8\u30eb (\u591a\u9805\u5f0f\u306e\u4fc2\u6570) \u3068\u306a\u308b.<\/p>\n

\u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593\u306b\u304a\u3044\u3066\u3082, 6.1.1 \u591a\u9805\u5f0f\u88dc\u9593\u3068\u540c\u69d8\u306b \\(x_0, x_1, \\dots, x_n\\) \u304c\u76f8\u7570\u306a\u308b\u70b9\u3067\u3042\u308c\u3070\u3053\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306f\u89e3\u3092\u6301\u3064. \u3057\u304b\u3057\u306a\u304c\u3089, \u3084\u306f\u308a\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u8a08\u7b97\u6cd5\u306f\u65b9\u7a0b\u5f0f\u306e\u6761\u4ef6\u6570\u306a\u3069\u306e\u70b9\u304b\u3089\u597d\u307e\u3057\u304f\u306a\u304f, \u30cb\u30e5\u30fc\u30c8\u30f3\u88dc\u9593\u306b\u4f3c\u305f\u4ee5\u4e0b\u306e\u8a08\u7b97\u6cd5\u304c\u7528\u3044\u3089\u308c\u308b.<\/p>\n

n + 1 \u500b\u306e\u6a19\u672c\u70b9 \\(x_0, x_1, \\dots, x_n\\) \u304c\u3042\u308b\u3068\u304d\u306b, \\(j = 0 \\sim n\\) \u306b\u3064\u3044\u3066
\n\\[
\n\\begin{align}
\n& u_{2j} = x_j \\\\
\n& u_{2j+1} = x_j \\\\
\n\\end{align}
\n\\]\n\u3068\u3059\u308b.<\/p>\n

\u5dee\u5206\u5546\u306e\u8a08\u7b97\u3092\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b.
\n\\[
\n\\begin{align}
\n& f[u_i] = f(u_i) (i = 0 \\sim 2n+1) \\\\
\n& f[u_i, u_{i+1}] = f'(u_i) (i = 0, 2, \\dots, 2n) \\\\
\n& f[u_i, u_{i+1}] = (f[u_{i+1}] – f[u_i])\/(u_{i+1} – u_i) (i = 1, 3, \\dots, 2n-1) \\\\
\n& f[u_i, \\dots, u_{i+k}] = (f[u_{i+1}, \\dots, u_{i+k}] – f[u_i, \\dots, u_{i+k-1}])\/(u_{i+k} – u_i) (k = 2 \\sim 2n + 1, i = 0 \\sim 2n + 1 – k) \\\\
\n\\end{align}
\n\\]\n\u95a2\u6570 \\(f(x)\\) \u306e\u88dc\u9593\u5024\u306f\u6b21\u5f0f\u3067\u6c42\u3081\u3089\u308c\u308b.
\n\\[
\n\\begin{align}
\nf(x) & = f[u_0] \\\\
\n& + (x – u_0)f[u_0, u_1] \\\\
\n& + (x – u_0)(x – u_1)f[u_0, u_1, u_2] \\\\
\n& + \\dots \\\\
\n& + (x – u_0)(x – u_1) \\dots (x – u_{2n+1})f[u_0, u_1, \\dots, u_{2n+1}] \\\\
\n\\end{align}
\n\\]\n

6.2.2 \u6570\u5024\u5b9f\u9a13<\/h3>\n

6.1.2 \u3068\u540c\u69d8\u306b, \u533a\u9593 \\([-1, 1]\\) \u306b\u304a\u3044\u3066\u6b21\u306e\u6307\u6570\u95a2\u6570\u3092\u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593\u3059\u308b.
\n\\[
\nf(x) = 2e^{x-1} – 1
\n\\]\n\\(n = 2 \\sim 5\\) \u3068\u3057\u3066 (\u3059\u306a\u308f\u3061, \\(5 \\sim 11\\) \u6b21\u591a\u9805\u5f0f\u3092\u7528\u3044\u3066) \u88dc\u9593\u3092\u884c\u3046. \u305f\u3060\u3057, \u533a\u9593 \\([-1, 1]\\) \u3092 \\(n\\) \u7b49\u5206\u3057\u3066, \u4e21\u7aef\u3092\u542b\u3081\u7b49\u9593\u9694\u306b\u4e26\u3093\u3060 \\(n + 1\\) \u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u5024\u304a\u3088\u3073\u5fae\u5206\u5024\u3092\u30c7\u30fc\u30bf\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b.<\/p>\n

\"\"<\/p>\n

\u7e26\u8ef8\u3092\u8aa4\u5dee (\u88dc\u9593\u5024 – \u53b3\u5bc6\u5024) \u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n

\"\"<\/p>\n

\u540c\u3058\u6a19\u672c\u70b9\u6570\u306e\u3068\u304d\u306b\u306f, \u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593\u591a\u9805\u5f0f\u306e\u6b21\u6570\u306f\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u591a\u9805\u5f0f\u306e\u500d\u306b\u306a\u308b\u305f\u3081\u7cbe\u5ea6\u304c\u3088\u3044. 1 \u3064\u306e\u6a19\u672c\u70b9\u306b\u304a\u3044\u3066, \u95a2\u6570\u5024\u306b\u52a0\u3048\u3066\u5fae\u5206\u5024\u3082\u5bb9\u6613\u306b\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306a\u3089\u3070\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u3088\u308a\u6709\u5229\u3068\u601d\u308f\u308c\u308b.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u88dc\u9593\u516c\u5f0f\u306f\u6a19\u672c\u70b9\u306b\u304a\u3044\u3066\u95a2\u6570\u5024\u304c\u4e00\u81f4\u3059\u308b\u8fd1\u4f3c\u5f0f\u3092\u4e0e\u3048\u305f. \u3053\u308c\u306b\u5bfe\u3057\u3066, \u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593\u306f\u3084\u306f\u308a\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u304c\u6a19\u672c\u70b9\u306b\u304a\u3044\u3066\u95a2\u6570\u5024\u306e\u4ed6\u306b\u5fae\u5206\u5024\u3082\u4e00\u81f4\u3059\u308b\u8fd1\u4f3c\u5f0f\u3092\u4e0e\u3048\u308b. 6.2.1 \u30a8\u30eb\u30df\u30fc\u30c8\u88dc\u9593 \u533a\u9593 […]<\/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,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-5423","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5423","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/comments?post=5423"}],"version-history":[{"count":11,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5423\/revisions"}],"predecessor-version":[{"id":5487,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/5423\/revisions\/5487"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=5423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=5423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=5423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}