{"id":1643,"date":"2026-10-28T10:00:00","date_gmt":"2026-10-28T01:00:00","guid":{"rendered":"https:\/\/quantumsea.net\/?p=1643"},"modified":"2026-10-25T10:22:55","modified_gmt":"2026-10-25T01:22:55","slug":"qs-runge-polynomial-node-placement-20261025","status":"publish","type":"post","link":"https:\/\/quantumsea.net\/?p=1643","title":{"rendered":"\u30eb\u30f3\u30b2\u73fe\u8c61\u3001\u88dc\u9593\u3059\u308b\u70b9\u3092\u5897\u3084\u3057\u3066\u3082\u7aef\u306e\u8aa4\u5dee\u304c\u5927\u304d\u304f\u306a\u308b\u7406\u7531"},"content":{"rendered":"<p>\u6e2c\u5b9a\u3057\u305f\u70b9\u3092\u3059\u3079\u3066\u901a\u308b\u6ed1\u3089\u304b\u306a\u66f2\u7dda\u3092\u63cf\u304d\u305f\u3044\u3002\u305d\u306e\u305f\u3081\u306b\u70b9\u3092\u5897\u3084\u3057\u3001\u3088\u308a\u9ad8\u3044\u6b21\u6570\u306e\u591a\u9805\u5f0f\u3092\u4f7f\u3048\u3070\u3001\u70b9\u3068\u70b9\u306e\u9593\u3082\u6b63\u78ba\u306b\u306a\u308b\u3088\u3046\u306b\u601d\u3048\u307e\u3059\u3002\u3068\u3053\u308d\u304c\u3001\u7b49\u9593\u9694\u306b\u4e26\u3079\u305f\u70b9\u3092\u4e00\u3064\u306e\u591a\u9805\u5f0f\u3067\u7d50\u3076\u3068\u3001\u70b9\u3067\u306f\u3074\u3063\u305f\u308a\u5408\u3063\u3066\u3044\u308b\u306e\u306b\u3001\u533a\u9593\u306e\u7aef\u306b\u8fd1\u3044\u5834\u6240\u3067\u5927\u304d\u304f\u5916\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30eb\u30f3\u30b2\u73fe\u8c61<\/strong>\u306f\u3001\u591a\u9805\u5f0f\u88dc\u9593\u3067\u70b9\u6570\u3092\u5897\u3084\u3057\u305f\u3068\u304d\u306b\u3001\u3053\u3046\u3057\u305f\u632f\u308c\u304c\u60aa\u5316\u3057\u5f97\u308b\u3053\u3068\u3092\u793a\u3059\u4f8b\u3067\u3059\u3002\u70b9\u3092\u5897\u3084\u3059\u52b9\u679c\u306f\u3001\u305d\u306e\u6570\u3060\u3051\u3067\u306f\u6c7a\u307e\u308a\u307e\u305b\u3093\u3002\u3053\u3053\u3067\u306f\u540c\u3058\u95a2\u6570\u3092\u3001\u7b49\u9593\u9694\u306e\u70b9\u3068\u3001\u4e21\u7aef\u306b\u70b9\u3092\u96c6\u3081\u305f\u914d\u7f6e\u3067\u8a08\u7b97\u3057\u3001\u4f55\u304c\u9055\u3046\u306e\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<section class=\"influvetor-quick-summary\" aria-label=\"\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f\">\n<p><strong>\u7c21\u5358\u306b\u307e\u3068\u3081\u308b\u3068\uff1f<\/strong><\/p>\n<ul>\n<li>n+1\u500b\u306e\u7570\u306a\u308b\u70b9\u3092\u901a\u308b\u3001\u6b21\u6570n\u4ee5\u4e0b\u306e\u591a\u9805\u5f0f\u306f\u4e00\u3064\u306b\u5b9a\u307e\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u70b9\u3067\u4e00\u81f4\u3059\u308b\u3053\u3068\u3068\u3001\u305d\u306e\u9593\u306e\u8aa4\u5dee\u304c\u5c0f\u3055\u3044\u3053\u3068\u306f\u5225\u3067\u3059\u3002<\/li>\n<li>\u4eca\u56de\u306e\u6ed1\u3089\u304b\u306a\u95a2\u6570\u3067\u306f\u3001\u7b49\u9593\u9694\u306e\u70b9\u309211\u500b\u304b\u308921\u500b\u3078\u5897\u3084\u3059\u3068\u3001\u8a55\u4fa1\u3057\u305f\u5834\u6240\u3067\u306e\u6700\u5927\u8aa4\u5dee\u306f\u7d041.92\u304b\u3089\u7d0459.8\u3078\u5897\u3048\u307e\u3057\u305f\u3002<\/li>\n<li>\u4e21\u7aef\u3092\u5bc6\u306b\u3057\u305fChebyshev\u2013Lobatto\u70b9\u3067\u306f\u3001\u540c\u3058\u6bd4\u8f03\u3067\u8aa4\u5dee\u304c\u7d040.132\u304b\u3089\u7d040.0177\u3078\u6e1b\u308a\u307e\u3059\u3002\u70b9\u3092\u9078\u3079\u306a\u3044\u5834\u5408\u306f\u3001\u533a\u5206\u7684\u306a\u4f4e\u6b21\u88dc\u9593\u306a\u3069\u3082\u5019\u88dc\u306b\u306a\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/section>\n<h2>\u70b9\u3092\u901a\u308b\u3068\u3044\u3046\u7d04\u675f\u306f\u3001\u70b9\u306e\u9593\u307e\u3067\u53ca\u3070\u306a\u3044<\/h2>\n<p><strong>\u88dc\u9593<\/strong>\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u4f4d\u7f6e\u3067\u4e0e\u3048\u3089\u308c\u305f\u5024\u306b\u4e00\u81f4\u3059\u308b\u95a2\u6570\u3092\u4f5c\u308b\u64cd\u4f5c\u3067\u3059\u3002\u4f8b\u3048\u307011\u500b\u306e\u7570\u306a\u308b\u4f4d\u7f6e\u3067\u5024\u304c\u5206\u304b\u3063\u3066\u3044\u308c\u3070\u3001\u305d\u306e\u3059\u3079\u3066\u3092\u901a\u308b10\u6b21\u4ee5\u4e0b\u306e\u591a\u9805\u5f0f\u3092\u4e00\u610f\u306b\u6c7a\u3081\u3089\u308c\u307e\u3059\u300221\u500b\u306a\u308920\u6b21\u4ee5\u4e0b\u3067\u3059\u3002\u591a\u9805\u5f0f\u3068\u306f\u3001\u5b9a\u6570\u3001x\u3001x\u00b2\u306a\u3069\u3092\u4fc2\u6570\u4ed8\u304d\u3067\u8db3\u3057\u5408\u308f\u305b\u305f\u5f0f\u3067\u3059\u3002[1][2]<\/p>\n<p>\u6b21\u6570\u3092\u4e0a\u3052\u308b\u3068\u3001\u66f2\u7dda\u306f\u591a\u304f\u306e\u70b9\u3092\u901a\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u4e00\u65b9\u3067\u3001\u533a\u9593\u5168\u4f53\u3092\u4e00\u3064\u306e\u5f0f\u3067\u7d50\u3076\u305f\u3081\u3001\u3042\u308b\u70b9\u306b\u5408\u308f\u305b\u308b\u305f\u3081\u306e\u8abf\u6574\u304c\u9060\u304f\u306e\u5f62\u306b\u3082\u95a2\u308f\u308a\u307e\u3059\u3002\u88dc\u9593\u70b9\u3067\u306f\u305a\u308c\u304c\u30bc\u30ed\u3067\u3082\u3001\u70b9\u3068\u70b9\u306e\u9593\u3067\u632f\u308c\u308b\u4f59\u5730\u304c\u6b8b\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3053\u3068\u306f\u3001\u88dc\u9593\u591a\u9805\u5f0f\u3092\u5404\u70b9\u306e\u5024\u306e\u91cd\u307f\u4ed8\u304d\u548c\u3068\u3057\u3066\u898b\u308b\u3068\u5206\u304b\u308a\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002\u91cd\u307f\u306f\u5834\u6240x\u306b\u3088\u3063\u3066\u5909\u308f\u308a\u3001\u7279\u5b9a\u306e\u88dc\u9593\u70b9\u3067\u306f\u3001\u305d\u306e\u70b9\u306e\u91cd\u307f\u3060\u3051\u304c1\u3001\u307b\u304b\u306f0\u306b\u306a\u308a\u307e\u3059\u3002\u70b9\u306e\u9593\u3067\u306f\u91cd\u307f\u304c\u8ca0\u306b\u306a\u308b\u3053\u3068\u3082\u3001\u7d76\u5bfe\u5024\u304c1\u3092\u8d85\u3048\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u5358\u7d14\u306b\u96a3\u306e\u4e8c\u70b9\u3092\u6df7\u305c\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u7b49\u9593\u9694\u306e\u9ad8\u6b21\u88dc\u9593\u3067\u306f\u3001\u7279\u306b\u7aef\u306e\u8fd1\u304f\u3067\u5927\u304d\u306a\u91cd\u307f\u304c\u73fe\u308c\u3001\u66f2\u7dda\u306e\u632f\u308c\u3084\u5165\u529b\u8aa4\u5dee\u306e\u5897\u5e45\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002[1]<\/p>\n<h2>\u6ed1\u3089\u304b\u306a\u5c71\u3092\u300111\u70b9\u306821\u70b9\u3067\u7d50\u3076<\/h2>\n<p>\u6bd4\u8f03\u3059\u308b\u306e\u306f\u3001\u533a\u9593\u22121\u2266x\u22661\u306e\u95a2\u6570<strong>f(x)=1\/(1+25x\u00b2)<\/strong>\u3067\u3059\u3002\u4e2d\u592ex=0\u30671\u306b\u306a\u308a\u3001\u4e21\u7aef\u3067\u306f1\/26\u306b\u306a\u308b\u3001\u6ed1\u3089\u304b\u306a\u5c71\u306e\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002\u6e2c\u5b9a\u30ce\u30a4\u30ba\u3092\u52a0\u3048\u305a\u3001\u3053\u306e\u5f0f\u304b\u3089\u5f97\u305f\u5024\u3092\u88dc\u9593\u70b9\u306b\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<p>\u7b49\u9593\u9694\u306e\u5834\u5408\u300111\u70b9\u306f0.2\u523b\u307f\u300121\u70b9\u306f0.1\u523b\u307f\u3067\u3059\u3002\u305d\u308c\u305e\u308c\u3092\u4e00\u3064\u306e10\u6b21\u4ee5\u4e0b\u300120\u6b21\u4ee5\u4e0b\u306e\u591a\u9805\u5f0f\u3067\u7d50\u3073\u307e\u3057\u305f\u3002\u4f5c\u3063\u305f\u66f2\u7dda\u3068\u5143\u306e\u95a2\u6570\u306e\u5dee\u306f\u3001\u533a\u9593\u5185\u306e2,001\u304b\u6240\u30920.001\u523b\u307f\u3067\u8a55\u4fa1\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u3044\u3046\u6700\u5927\u8aa4\u5dee\u306f<strong>\u3053\u306e\u8a55\u4fa1\u70b9\u3067\u898b\u3064\u304b\u3063\u305f\u6700\u5927\u5024<\/strong>\u3067\u3042\u308a\u3001\u9023\u7d9a\u533a\u9593\u5168\u4f53\u306e\u53b3\u5bc6\u306a\u6700\u5927\u5024\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>11\u70b9\u306e\u6700\u5927\u7d76\u5bfe\u8aa4\u5dee\u306f\u7d041.92\u3067\u3057\u305f\u300221\u70b9\u3078\u5897\u3084\u3059\u3068\u7d0459.8\u306b\u306a\u308a\u3001\u8a55\u4fa1\u70b9\u306e\u4e00\u3064x=\u22120.975\u4ed8\u8fd1\u3067\u5927\u304d\u304f\u5916\u308c\u307e\u3059\u3002\u5143\u306e\u95a2\u6570\u304c0\u304b\u30891\u306e\u9593\u306b\u53ce\u307e\u308b\u306e\u306b\u3001\u88dc\u9593\u66f2\u7dda\u306f\u7aef\u306e\u8fd1\u304f\u3067\u5927\u304d\u304f\u8ca0\u306e\u5074\u3078\u632f\u308c\u3066\u3044\u307e\u3059\u3002\u7aef\u70b9\u305d\u306e\u3082\u306e\u3082\u88dc\u9593\u70b9\u306a\u306e\u3067\u3001x=\u22121\u3068x=1\u3067\u306f\u6b63\u3057\u3044\u5024\u306b\u623b\u308a\u307e\u3059\u3002\u554f\u984c\u306f\u3001\u7aef\u70b9\u3068\u305d\u306e\u96a3\u306e\u70b9\u306e\u9593\u306b\u3082\u73fe\u308c\u308b\u306e\u3067\u3059\u3002<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-runge-polynomial-node-placement-20261025-figure-0703928a080b.png\" alt=\"\u540c\u3058\u95a2\u6570\u3092\u7b49\u9593\u9694\u70b9\u3068Chebyshev\u2013Lobatto\u70b9\u3067\u88dc\u9593\u3057\u305f\u72ec\u81ea\u8a08\u7b97\u3002\u4e0a\u6bb5\u3067\u306f20\u6b21\u306e\u66f2\u7dda\u304c\u7aef\u306e\u8fd1\u304f\u3067\u7d04\u30de\u30a4\u30ca\u30b960\u307e\u3067\u632f\u308c\u308b\u3002\u4e0b\u6bb5\u306f\u4e21\u7aef\u306b\u70b9\u3092\u96c6\u3081\u305f\u914d\u7f6e\u3067\u3001\u5143\u306e\u5c71\u306e\u5f62\u306b\u8fd1\u3065\u304f\u3002\u4e0a\u4e0b\u306e\u7e26\u8ef8\u306e\u7bc4\u56f2\u306f\u7570\u306a\u308b\u3002\" style=\"max-width:100%;height:auto\"\/><figcaption>\u72ec\u81ea\u8a08\u7b97\u306b\u3088\u308b\u6bd4\u8f03\u3002\u7070\u8272\u304c\u5143\u306e\u95a2\u6570\u3001\u9752\u304c10\u6b21\u4ee5\u4e0b\u3001\u6a59\u304c20\u6b21\u4ee5\u4e0b\u306e\u88dc\u9593\u591a\u9805\u5f0f\u3001\u9ed2\u70b9\u304c21\u500b\u306e\u88dc\u9593\u70b9\u3067\u3059\u3002\u4e0a\u6bb5\u306f\u7b49\u9593\u9694\u3001\u4e0b\u6bb5\u306fChebyshev\u2013Lobatto\u70b9\u3002\u4e0a\u4e0b\u3067\u7e26\u8ef8\u306e\u7bc4\u56f2\u304c\u7570\u306a\u308a\u307e\u3059\u3002Decimal\u306e80\u6841\u8a08\u7b97\u3092\u7528\u3044\u300160\u6841\u8a08\u7b97\u3068\u5225\u5f62\u5f0f\u306e\u8a55\u4fa1\u3067\u3082\u7167\u5408\u3057\u307e\u3057\u305f\u3002\u5b9f\u6e2c\u30c7\u30fc\u30bf\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/figcaption><\/figure>\n<h2>\u540c\u3058\u70b9\u6570\u3067\u3082\u3001\u4e21\u7aef\u3092\u5bc6\u306b\u3059\u308b\u3068\u5909\u308f\u308b<\/h2>\n<p>\u6b21\u306b\u70b9\u306e\u4f4d\u7f6e\u3060\u3051\u3092\u5909\u3048\u307e\u3059\u3002\u4f7f\u3046\u306e\u306f<strong>Chebyshev\u2013Lobatto\u70b9<\/strong>\u3067\u3001Chebyshev\u306e\u7b2c2\u7a2e\u306e\u70b9\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002\u533a\u9593[\u22121,1]\u3067\u306f\u3001k=0,\u2026,n\u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u7f6e\u304d\u307e\u3059\u3002[1][2]<\/p>\n<p><strong>x<sub>k<\/sub>=\u2212cos(k\u03c0\/n)<\/strong><\/p>\n<p>\u534a\u5186\u4e0a\u306b\u7b49\u9593\u9694\u306b\u4e26\u3079\u305f\u70b9\u3092\u3001\u6a2a\u8ef8\u3078\u5782\u76f4\u306b\u843d\u3068\u3057\u305f\u914d\u7f6e\u3068\u8003\u3048\u308b\u3068\u3001\u4e21\u7aef\u3067\u9593\u9694\u304c\u72ed\u304f\u306a\u308b\u7406\u7531\u304c\u898b\u3048\u307e\u3059\u3002\u4e2d\u592e\u306e\u9593\u9694\u306f\u5e83\u304f\u3001\u7aef\u3078\u884c\u304f\u307b\u3069\u70b9\u304c\u96c6\u307e\u308a\u307e\u3059\u3002\u533a\u9593\u306e\u4e21\u7aef\u3082\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u914d\u7f6e\u3067\u540c\u3058\u95a2\u6570\u3092\u88dc\u9593\u3059\u308b\u3068\u300111\u70b9\u306e\u6700\u5927\u7d76\u5bfe\u8aa4\u5dee\u306f\u7d040.132\u300121\u70b9\u3067\u306f\u7d040.0177\u3067\u3057\u305f\u3002\u7b49\u9593\u9694\u306e21\u70b9\u3088\u308a\u3001Chebyshev\u2013Lobatto\u306e11\u70b9\u306e\u307b\u3046\u304c\u3001\u3053\u306e\u4f8b\u3067\u306f\u5c0f\u3055\u306a\u8aa4\u5dee\u306b\u306a\u308a\u307e\u3059\u3002\u70b9\u306e\u6570\u3060\u3051\u3067\u7cbe\u5ea6\u3092\u6bd4\u8f03\u3067\u304d\u306a\u3044\u3053\u3068\u304c\u3001\u540c\u3058\u95a2\u6570\u30fb\u540c\u3058\u8a55\u4fa1\u4f4d\u7f6e\u3067\u8868\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e21\u7aef\u3092\u5bc6\u306b\u3059\u308b\u914d\u7f6e\u306f\u3001\u533a\u9593\u306e\u7aef\u3067\u5927\u304d\u304f\u306a\u308a\u3084\u3059\u3044\u88dc\u9593\u306e\u4e0d\u5b89\u5b9a\u3055\u3092\u6291\u3048\u308b\u52a9\u3051\u306b\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u3069\u3093\u306a\u95a2\u6570\u3067\u3082\u6709\u9650\u500b\u306e\u70b9\u3067\u6b63\u78ba\u306b\u306a\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6025\u306a\u5909\u5316\u3084\u6ed1\u3089\u304b\u3067\u306a\u3044\u90e8\u5206\u304c\u3042\u308c\u3070\u3001\u305d\u308c\u306b\u5fdc\u3058\u305f\u70b9\u6570\u3084\u5225\u306e\u8fd1\u4f3c\u65b9\u6cd5\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n<h2>\u8a08\u7b97\u306e\u6841\u6570\u3092\u5897\u3084\u3057\u3066\u3082\u3001\u88dc\u9593\u306e\u5f62\u306f\u5909\u308f\u3089\u306a\u3044<\/h2>\n<p>\u5927\u304d\u306a\u632f\u308c\u3092\u898b\u308b\u3068\u3001\u8a08\u7b97\u9014\u4e2d\u306e\u4e38\u3081\u304c\u539f\u56e0\u306b\u601d\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u4eca\u56de\u306e\u8a08\u7b97\u3067\u306f\u3001\u91cd\u5fc3\u5f62\u5f0f\u3068\u547c\u3070\u308c\u308b\u88dc\u9593\u306e\u8a55\u4fa1\u5f0f\u3092\u4f7f\u3044\u300160\u6841\u306880\u6841\u3067\u7d50\u679c\u3092\u6bd4\u3079\u307e\u3057\u305f\u30022,001\u304b\u6240\u306e\u6bd4\u8f03\u5dee\u306f3\u00d710<sup>\u221255<\/sup>\u672a\u6e80\u3067\u300120\u6b21\u306e\u7b49\u9593\u9694\u88dc\u9593\u306e\u5927\u304d\u306a\u632f\u308c\u306f\u6b8b\u308a\u307e\u3057\u305f\u3002\u3055\u3089\u306b\u3001Newton\u306e\u5dee\u5206\u5546\u304b\u3089\u7d44\u307f\u7acb\u3066\u308b\u5225\u5f62\u5f0f\u3067\u3082\u8a55\u4fa1\u70b9\u3092\u629c\u304d\u51fa\u3057\u3066\u7167\u5408\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u306f\u3001\u3053\u306e\u4f8b\u3067\u8d77\u304d\u3066\u3044\u308b\u632f\u308c\u304c\u3001\u5358\u306b\u8a08\u7b97\u306e\u6841\u6570\u4e0d\u8db3\u3067\u306f\u306a\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u70b9\u3092\u901a\u308b\u4e00\u3064\u306e\u591a\u9805\u5f0f\u3068\u3057\u3066\u6c7a\u307e\u3063\u305f\u5f62\u304c\u3001\u70b9\u306e\u9593\u3067\u5143\u306e\u95a2\u6570\u304b\u3089\u96e2\u308c\u3066\u3044\u307e\u3059\u3002\u8a08\u7b97\u65b9\u6cd5\u3092\u5b89\u5b9a\u3055\u305b\u308b\u3053\u3068\u3068\u3001\u8fd1\u4f3c\u306b\u9069\u3057\u305f\u70b9\u3084\u95a2\u6570\u306e\u5f62\u3092\u9078\u3076\u3053\u3068\u306f\u3001\u4e21\u65b9\u5fc5\u8981\u3067\u3059\u3002[1]<\/p>\n<h2>\u70b9\u3092\u9078\u3079\u308b\u5834\u5408\u3068\u3001\u6e2c\u5b9a\u6e08\u307f\u306e\u5834\u5408<\/h2>\n<p>\u95a2\u6570\u3092\u597d\u304d\u306a\u4f4d\u7f6e\u3067\u8a08\u7b97\u3067\u304d\u308b\u306a\u3089\u3001\u7aef\u3092\u5bc6\u306b\u3057\u305f\u70b9\u914d\u7f6e\u3092\u521d\u3081\u304b\u3089\u9078\u3079\u307e\u3059\u3002\u3068\u3053\u308d\u304c\u3001\u3059\u3067\u306b\u7b49\u9593\u9694\u3067\u63a1\u3063\u305f\u6e2c\u5b9a\u5024\u3057\u304b\u306a\u3044\u5834\u5408\u306f\u3001\u70b9\u306e\u6a2a\u5ea7\u6a19\u3060\u3051\u3092Chebyshev\u70b9\u306b\u4ed8\u3051\u66ff\u3048\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u305d\u306e\u5834\u6240\u3067\u6e2c\u3063\u305f\u5024\u3067\u306f\u306a\u304f\u306a\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u305d\u306e\u5834\u5408\u306f\u3001\u96a3\u63a5\u3059\u308b\u5c11\u6570\u306e\u70b9\u3092\u533a\u9593\u3054\u3068\u306b\u7d50\u3076\u65b9\u6cd5\u3084\u3001\u30b9\u30d7\u30e9\u30a4\u30f3\u306e\u3088\u3046\u306a\u533a\u5206\u7684\u306a\u4f4e\u6b21\u591a\u9805\u5f0f\u3092\u691c\u8a0e\u3067\u304d\u307e\u3059\u3002\u5168\u70b9\u3092\u4e00\u3064\u306e\u9ad8\u6b21\u5f0f\u3078\u62bc\u3057\u8fbc\u3080\u4ee5\u5916\u306b\u3082\u3001\u88dc\u9593\u306e\u7d44\u307f\u7acb\u3066\u65b9\u304c\u3042\u308a\u307e\u3059\u3002Chebfun\u306e\u516c\u5f0f\u4f8b\u3067\u3082\u3001\u7b49\u9593\u9694\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u5358\u7d14\u306a\u591a\u9805\u5f0f\u88dc\u9593\u3068\u306f\u7570\u306a\u308b\u8fd1\u4f3c\u3092\u4f7f\u3044\u3001\u7aef\u3067\u306e\u632f\u308c\u3092\u6bd4\u8f03\u3057\u3066\u3044\u307e\u3059\u3002[3]<\/p>\n<p>\u5b9f\u30c7\u30fc\u30bf\u3092\u6271\u3046\u3068\u304d\u306f\u3001\u66f2\u7dda\u304c\u65e2\u77e5\u306e\u70b9\u3092\u901a\u308b\u304b\u3060\u3051\u3067\u306a\u304f\u3001\u88dc\u9593\u306b\u4f7f\u308f\u306a\u304b\u3063\u305f\u70b9\u3084\u7aef\u306b\u8fd1\u3044\u9818\u57df\u3067\u3082\u8aa4\u5dee\u3092\u8abf\u3079\u308b\u3053\u3068\u304c\u5927\u5207\u3067\u3059\u3002\u30ce\u30a4\u30ba\u304c\u3042\u308b\u306a\u3089\u3001\u5168\u70b9\u3078\u306e\u5b8c\u5168\u4e00\u81f4\u3088\u308a\u3001\u5e73\u6ed1\u5316\u3084\u8fd1\u4f3c\u306e\u8aa4\u5dee\u3092\u8a31\u3059\u307b\u3046\u304c\u76ee\u7684\u306b\u5408\u3046\u5834\u5408\u3082\u3042\u308a\u307e\u3059\u3002\u30eb\u30f3\u30b2\u73fe\u8c61\u304b\u3089\u5f97\u3089\u308c\u308b\u5224\u65ad\u6750\u6599\u306f\u3001\u70b9\u3092\u5897\u3084\u3059\u524d\u306b\u3001\u70b9\u306e\u7f6e\u304d\u65b9\u3068\u70b9\u306e\u9593\u3092\u7d50\u3076\u65b9\u6cd5\u3092\u4e00\u7dd2\u306b\u8003\u3048\u308b\u3053\u3068\u3067\u3059\u3002<\/p>\n<h2>\u51fa\u5178<\/h2>\n<ol>\n<li>Tobin A. Driscoll\u30fbRichard J. Braun\u3001<a href=\"https:\/\/fncbook.com\/python\/stability-1\/\">Fundamentals of Numerical Computation, 9.3 Stability of polynomial interpolation<\/a>\u3002\u88dc\u9593\u306e\u6761\u4ef6\u3001\u7b49\u9593\u9694\u70b9\u306e\u4e0d\u5b89\u5b9a\u6027\u3001Chebyshev\u70b9\u3002\u53d6\u5f97\u6642\u70b9\u306ePython\u7248\u3002<\/li>\n<li>Lloyd N. Trefethen\u3001<a href=\"https:\/\/www.chebfun.org\/docs\/guide\/guide04.html\">Chebfun Guide, Chapter 4: Chebfun and Approximation Theory<\/a>\u30014.1\u30fb4.3\u3002\u7b2c2\u7a2eChebyshev\u70b9\u306e\u5b9a\u7fa9\u3068\u591a\u9805\u5f0f\u88dc\u9593\u3002\u8868\u793a\u4e0a\u306e\u6700\u7d42\u6539\u8a02\u306f2019\u5e745\u6708\u3002<\/li>\n<li>Nick Trefethen\u3001<a href=\"https:\/\/www.chebfun.org\/examples\/approx\/EquispacedData.html\">Chebfuns from equispaced data<\/a>\u30012015\u5e744\u6708\u3002\u7b49\u9593\u9694\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u88dc\u9593\u30fb\u8fd1\u4f3c\u306e\u6bd4\u8f03\u3002\u3044\u305a\u308c\u30822026\u5e7410\u670825\u65e5\u53d6\u5f97\u3002\u672c\u6587\u306e\u6570\u5024\u4f8b\u3068\u56f3\u306f\u3001\u672c\u6587\u306b\u793a\u3057\u305f\u6761\u4ef6\u3067\u306e\u72ec\u81ea\u8a08\u7b97\u3067\u3059\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6e2c\u5b9a\u3057\u305f\u70b9\u3092\u3059\u3079\u3066\u901a\u308b\u6ed1\u3089\u304b\u306a\u66f2\u7dda\u3092\u63cf\u304d\u305f\u3044\u3002\u305d\u306e\u305f\u3081\u306b\u70b9\u3092\u5897\u3084\u3057\u3001\u3088\u308a\u9ad8\u3044\u6b21\u6570\u306e\u591a\u9805\u5f0f\u3092\u4f7f\u3048\u3070\u3001\u70b9\u3068\u70b9\u306e\u9593\u3082\u6b63\u78ba\u306b\u306a\u308b\u3088\u3046\u306b\u601d\u3048\u307e\u3059\u3002\u3068\u3053\u308d\u304c\u3001\u7b49\u9593\u9694\u306b\u4e26\u3079\u305f\u70b9\u3092\u4e00\u3064\u306e\u591a\u9805\u5f0f\u3067\u7d50\u3076\u3068\u3001\u70b9\u3067\u306f\u3074\u3063\u305f\u308a\u5408\u3063\u3066\u3044\u308b\u306e\u306b\u3001\u533a\u9593 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1641,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":false,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[31],"tags":[333],"class_list":["post-1643","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-software","tag-runge-phenomenon"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/quantumsea.net\/wp-content\/uploads\/2026\/10\/qs-runge-polynomial-node-placement-20261025-featured-fb5df14559b8.png","_links":{"self":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1643","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1643"}],"version-history":[{"count":1,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1643\/revisions"}],"predecessor-version":[{"id":1644,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/posts\/1643\/revisions\/1644"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=\/wp\/v2\/media\/1641"}],"wp:attachment":[{"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantumsea.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}