{"id":3241,"date":"2026-08-25T17:31:29","date_gmt":"2026-08-25T08:31:29","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=3241"},"modified":"2026-09-12T22:10:21","modified_gmt":"2026-09-12T13:10:21","slug":"5_sparse","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/5_sparse\/","title":{"rendered":"5. \u5927\u898f\u6a21\u758e\u884c\u5217\u306e\u7dda\u5f62\u8a08\u7b97"},"content":{"rendered":"<h3>\u306f\u3058\u3081\u306b<\/h3>\n<p>\u884c\u5217\u306e\u8981\u7d20\u306e\u3046\u3061\u591a\u304f\u304c 0 \u3067\u3042\u308b\u3088\u3046\u306a\u884c\u5217\u3092<strong>\u758e\u884c\u5217<\/strong>\u3068\u3044\u3046. \u3053\u308c\u306b\u5bfe\u3057\u3066, \u884c\u5217\u306e\u8981\u7d20\u306e\u3046\u3061\u307b\u3068\u3093\u3069\u304c 0 \u3067\u306a\u3044\u901a\u5e38\u306e\u884c\u5217\u3092, \u758e\u884c\u5217\u3068\u533a\u5225\u3057\u305f\u3044\u5834\u5408\u306b\u306f, <strong>\u5bc6\u884c\u5217<\/strong>\u3068\u3088\u3076.<\/p>\n<p>\u758e\u884c\u5217\u306f\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u305f\u3081\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u4fc2\u6570\u306a\u3069\u3068\u3057\u3066\u3088\u304f\u73fe\u308f\u308c\u308b. \u305d\u306e\u969b\u306b\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u7cbe\u5ea6\u3092\u4e0a\u3052\u308b\u305f\u3081\u306b\u306f\u5927\u898f\u6a21\u306a\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u304c\u5fc5\u8981\u306b\u306a\u308b\u305f\u3081, \u4e00\u822c\u306b\u5927\u898f\u6a21\u306a\u884c\u5217 (\u4f8b\u3048\u3070, \u300c\u6570\u4e07 \u00d7 \u6570\u4e07\u300d\u4ee5\u4e0a) \u304c\u5fc5\u8981\u3068\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044.<\/p>\n<p>\u901a\u5e38\u306e\u5bc6\u884c\u5217\u306f 2 \u6b21\u5143\u914d\u5217\u3067\u8868\u3059\u306e\u304c\u666e\u901a\u3067\u3042\u308b. \u3057\u304b\u3057, \u758e\u884c\u5217\u3092\u540c\u69d8\u306b 2 \u6b21\u5143\u914d\u5217\u3067\u8868\u3059\u3068 0 \u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u591a\u304f\u306e\u30e1\u30e2\u30ea\u30fc\u304c\u6d88\u8cbb\u3055\u308c, \u8a08\u7b97\u6642\u306b\u306f 0 \u3068\u306e\u6f14\u7b97\u306b\u591a\u304f\u306e CPU \u6642\u9593\u304c\u4f7f\u308f\u308c\u3066\u3057\u307e\u3046. \u305d\u308c\u3092\u907f\u3051\u308b\u305f\u3081\u306b\u758e\u884c\u5217\u5c02\u7528\u306e\u683c\u7d0d\u5f62\u5f0f\u304c\u4f7f\u308f\u308c\u308b.<\/p>\n<p>\u672c\u7ae0\u3067\u306f\u758e\u884c\u5217\u306e\u7dda\u5f62\u8a08\u7b97 (\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f, \u56fa\u6709\u5024\u554f\u984c\u306a\u3069) \u3092\u6271\u3046. \u758e\u884c\u5217\u306e\u7dda\u5f62\u8a08\u7b97\u3067\u306f, \u884c\u5217\u306e\u683c\u7d0d\u5f62\u5f0f\u304c\u7570\u306a\u308b\u3046\u3048\u306b\u9069\u7528\u3055\u308c\u308b\u554f\u984c\u306e\u6027\u8cea\u4e0a\u5927\u898f\u6a21\u3067\u3042\u308b\u3053\u3068\u304c\u591a\u3044\u305f\u3081, \u4f7f\u7528\u3055\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3082\u5f93\u6765\u306e\u5bc6\u884c\u5217\u7528\u306e\u7dda\u5f62\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u306f\u7570\u306a\u308b.<\/p>\n<h3>\u758e\u884c\u5217\u4fc2\u6570\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f<\/h3>\n<p>\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f Ax = b \u3092\u89e3\u304f\u3053\u3068\u3092\u8003\u3048\u308b. \u3053\u3053\u3067, A \u306f n x n \u758e\u884c\u5217, x \u304a\u3088\u3073 b \u306f n \u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b. A \u306f\u4fc2\u6570\u884c\u5217, x \u306f\u89e3\u30d9\u30af\u30c8\u30eb, b \u306f\u53f3\u8fba\u30d9\u30af\u30c8\u30eb\u3068\u3088\u3070\u308c\u308b.<\/p>\n<p>\u5fdc\u7528\u4f8b\u3068\u3057\u3066\u4ee3\u8868\u7684\u306a\u3082\u306e\u306f\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u3088\u304f\u73fe\u308c\u308b\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u554f\u984c\u3067\u3042\u308b. \u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5\u306f\u6700\u7d42\u7684\u306b\u758e\u884c\u5217\u4fc2\u6570\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306b\u5e30\u7740\u3055\u308c\u308b\u304c, \u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u9ad8\u7cbe\u5ea6\u3067\u6c42\u3081\u308b\u305f\u3081\u306b\u306f\u7d30\u304b\u306a\u96e2\u6563\u5316\u304c\u5fc5\u8981\u306b\u306a\u308a, \u4fc2\u6570\u884c\u5217\u306f\u975e\u5e38\u306b\u5927\u304d\u306a\u3082\u306e\u3068\u306a\u308b.<\/p>\n<p>\u305d\u306e\u305f\u3081, \u758e\u884c\u5217\u3092\u683c\u7d0d\u3059\u308b\u969b\u306b\u306f, \u5927\u898f\u6a21\u554f\u984c\u306b\u5bfe\u5fdc\u3067\u304d\u308b\u3088\u3046\u4f7f\u7528\u30e1\u30e2\u30ea\u30fc\u3092\u3067\u304d\u308b\u3060\u3051\u5c11\u306a\u304f\u3057 0 \u3067\u306a\u3044\u8981\u7d20\u3060\u3051\u3092\u683c\u7d0d\u3059\u308b\u3088\u3046\u306a\u5f62\u5f0f\u304c\u7528\u3044\u3089\u308c\u308b. <\/p>\n<p>\u5f93\u6765\u306e (\u5bc6\u884c\u5217\u7528\u306e) \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u76f4\u63a5\u89e3\u6cd5 (LU \u5206\u89e3\u3084\u30b3\u30ec\u30b9\u30ad\u30fc\u5206\u89e3) \u3067\u306f, \u4fc2\u6570\u884c\u5217\u304c\u758e\u3067\u3042\u3063\u3066\u3082\u8a08\u7b97\u3092\u9032\u3081\u3066\u3044\u304f\u3046\u3061\u306b\u3082\u3068\u3082\u3068 0 \u3060\u3063\u305f\u3068\u3053\u308d\u304c 0 \u3067\u306a\u304f\u306a\u3063\u3066\u3044\u304f (\u3053\u308c\u3092\u30d5\u30a3\u30eb\u30a4\u30f3\u3068\u3044\u3046). \u3053\u308c\u306f 0 \u3067\u306a\u3044\u8981\u7d20\u3060\u3051\u3092\u683c\u7d0d\u3059\u308b\u5f62\u5f0f\u306b\u3068\u3063\u3066\u306f\u4e0d\u90fd\u5408\u306a\u305f\u3081, \u758e\u884c\u5217\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306b\u306f\u30d5\u30a3\u30eb\u30a4\u30f3\u304c\u751f\u3058\u306a\u3044\u53cd\u5fa9\u6cd5\u304c\u9069\u3057\u3066\u3044\u308b. \u53cd\u5fa9\u6cd5\u3067\u306f\u4fc2\u6570\u884c\u5217\u306e\u975e\u30bc\u30ed\u8981\u7d20\u304c\u8a18\u61b6\u3055\u308c\u3066\u3044\u308b\u3068\u3053\u308d\u3060\u3051\u3067\u8a08\u7b97\u3092\u9032\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>\u53cd\u5fa9\u6cd5\u306b\u306f\u539f\u7406\u306e\u9055\u3044\u304b\u3089\u5b9a\u5e38\u53cd\u5fa9\u6cd5\u3068\u30af\u30ea\u30ed\u30d5\u90e8\u5206\u7a7a\u9593\u6cd5\u306e 2 \u3064\u304c\u3042\u308b.<\/p>\n<p>\u306a\u304a, \u4e00\u822c\u306e\u5bc6\u884c\u5217\u306b\u4f7f\u308f\u308c\u308b\u76f4\u63a5\u89e3\u6cd5 (LU \u5206\u89e3\u3084\u30b3\u30ec\u30b9\u30ad\u30fc\u5206\u89e3) \u306b\u3064\u3044\u3066\u3082, \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5de5\u592b\u3092\u51dd\u3089\u3057\u3066\u758e\u884c\u5217\u306b\u3046\u307e\u304f\u9069\u7528\u3059\u308b\u65b9\u6cd5\u3082\u958b\u767a\u3055\u308c\u3066\u3044\u308b.<\/p>\n<h3>\u758e\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c<\/h3>\n<p>\u56fa\u6709\u5024\u554f\u984c\u306f Ax = &lambda;x \u3092\u6e80\u305f\u3059 x \u3068 &lambda; \u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3042\u308b. \u3053\u3053\u3067, A \u306f n x n \u758e\u884c\u5217, x \u306f n \u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b. &lambda; \u306f\u56fa\u6709\u5024, x \u306f\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u3088\u3070\u308c\u308b.<\/p>\n<p>\u5927\u898f\u6a21\u758e\u884c\u5217\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u89e3\u6cd5\u3068\u3057\u3066\u306f, \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3068\u540c\u69d8\u306b 0 \u3067\u306a\u3044\u8981\u7d20\u3060\u3051\u3092\u7528\u3044\u3066\u8a08\u7b97\u3092\u9032\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u53cd\u5fa9\u6cd5\u304c\u4f7f\u308f\u308c\u308b. \u5bfe\u79f0\u884c\u5217\u7528\u306e\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5, \u975e\u5bfe\u79f0\u884c\u5217\u7528\u306e\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u306a\u3069\u304c\u3042\u308b.<\/p>\n<h2>\u76ee\u6b21<\/h2>\n<p><a href=\"\/jp\/num\/5-1_sparse\/\">5.1 \u758e\u884c\u5217\u306e\u683c\u7d0d\u5f62\u5f0f<\/a><br \/>\n<a href=\"\/jp\/num\/5-2_sparse\/\">5.2 \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f (\u5b9a\u5e38\u53cd\u5fa9\u6cd5)<\/a><br \/>\n<a href=\"\/jp\/num\/5-3_sparse\/\">5.3 \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f (\u30af\u30ea\u30ed\u30d5\u90e8\u5206\u7a7a\u9593\u6cd5)<\/a><br \/>\n5.4 \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f (\u76f4\u63a5\u89e3\u6cd5) (\u672a\u5b8c)<br \/>\n<a href=\"\/jp\/num\/5-5_sparse\/\">5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb<\/a><\/p>\n<hr\/>\n<h4>\u672c\u7ae0\u306e\u53c2\u8003\u6587\u732e<\/h4>\n[1] \u68ee\u53e3\u7e41\u4e00\u300c\u6570\u5024\u8a08\u7b97\u5de5\u5b66\u300d(1989) \u5ca9\u6ce2\u66f8\u5e97<br \/>\n[2] \u540d\u53d6\u4eae\u300c\u6570\u5024\u89e3\u6790\u3068\u305d\u306e\u5fdc\u7528\u300d\u30b3\u30ed\u30ca\u793e (1990)<br \/>\n[3] \u68ee\u6b63\u6b66, \u4ed6\u300c\u5ca9\u6ce2\u8b1b\u5ea7 \u5fdc\u7528\u6570\u5b6612 [\u65b9\u6cd52] \u7dda\u5f62\u8a08\u7b97\u300d\u5ca9\u6ce2\u66f8\u5e97 (1994)<br \/>\n[4] \u85e4\u91ce\u6e05\u6b21, \u4ed6\u300c\u53cd\u5fa9\u6cd5\u306e\u6570\u7406\u300d\u671d\u5009\u66f8\u5e97 (1996)<br \/>\n[5] R. Barrett, \u4ed6\u8457, \u9577\u8c37\u5ddd\u91cc\u7f8e, \u4ed6\u8a33\u300c\u53cd\u5fa9\u6cd5Templates\u300d\u671d\u5009\u66f8\u5e97 (1996)<br \/>\n[6] \u4ec1\u6728\u6ec9\u3001\u4ed6\u300c\u697d\u3057\u3044\u53cd\u5fa9\u6cd5\u300d\u5171\u7acb\u51fa\u7248 (1998)<br \/>\n[7] \u6749\u539f\u6b63\u9855, \u4ed6\u300c\u7dda\u5f62\u8a08\u7b97\u306e\u6570\u7406\u300d\u5ca9\u6ce2\u66f8\u5e97 (2009)<br \/>\n[8] F.\u30b7\u30e3\u30c8\u30e9\u30f3\u8457, \u4f0a\u7406\u6b63\u592b\u4ed6\u8a33\u300c\u884c\u5217\u306e\u56fa\u6709\u5024 \u65b0\u88c5\u7248\u300d\u4e38\u5584\u51fa\u7248 (2012)<br \/>\n[9] \u6afb\u4e95\u9244\u4e5f, \u4ed6\u300c\u6570\u5024\u7dda\u5f62\u4ee3\u6570\u306e\u6570\u7406\u3068HPC\u300d\u5171\u7acb\u51fa\u7248 (2018)<br \/>\n[10] Louis A. Hageman and David M. Young, &#8220;Applied Iterative Methods&#8221;. Academic Press, New York, 1981.<br \/>\n[11] Y. Saad, &#8220;Iterative methods for sparse linear systems&#8221; 2nd ed., SIAM (2003)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b \u884c\u5217\u306e\u8981\u7d20\u306e\u3046\u3061\u591a\u304f\u304c 0 \u3067\u3042\u308b\u3088\u3046\u306a\u884c\u5217\u3092\u758e\u884c\u5217\u3068\u3044\u3046. \u3053\u308c\u306b\u5bfe\u3057\u3066, \u884c\u5217\u306e\u8981\u7d20\u306e\u3046\u3061\u307b\u3068\u3093\u3069\u304c 0 \u3067\u306a\u3044\u901a\u5e38\u306e\u884c\u5217\u3092, \u758e\u884c\u5217\u3068\u533a\u5225\u3057\u305f\u3044\u5834\u5408\u306b\u306f, \u5bc6\u884c\u5217\u3068\u3088\u3076. \u758e\u884c\u5217\u306f\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3 [&hellip;]<\/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-3241","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u306f\u3058\u3081\u306b \u884c\u5217\u306e\u8981\u7d20\u306e\u3046\u3061\u591a\u304f\u304c 0 \u3067\u3042\u308b\u3088\u3046\u306a\u884c\u5217\u3092\u758e\u884c\u5217\u3068\u3044\u3046. \u3053\u308c\u306b\u5bfe\u3057\u3066, \u884c\u5217\u306e\u8981\u7d20\u306e\u3046\u3061\u307b\u3068\u3093\" \/>\n\t<meta name=\"robots\" content=\"max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n\t<meta name=\"author\" content=\"Administrator\"\/>\n\t<meta name=\"google-site-verification\" 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