{"id":48,"date":"2015-08-11T21:03:07","date_gmt":"2015-08-11T12:03:07","guid":{"rendered":"http:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/?page_id=48"},"modified":"2019-12-13T17:13:32","modified_gmt":"2019-12-13T08:13:32","slug":"research","status":"publish","type":"page","link":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/research\/","title":{"rendered":"\u7814\u7a76\u6210\u679c"},"content":{"rendered":"<ul style=\"list-style-type: circle\">\n<li><a href=\"#c\">\u751f\u547d\u73fe\u8c61\u306e\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0<\/a>\n<ul>\n<li><a href=\"#c02\">\u201c\u5148\u3092\u8aad\u3080\u201d\u30b3\u30a6\u30e2\u30ea\u306e\u4e09\u6b21\u5143\u98db\u884c\u7d4c\u8def\u8a08\u753b<\/a><\/li>\n<li><a href=\"#c01\">\u690d\u7269\u306e\u6982\u65e5\u6642\u8a08\u306b\u5bfe\u3059\u308b\u6570\u7406\u7684\u89e3\u6790<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#d\">\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0<\/a>\n<ul>\n<li><a href=\"#d01\">Kronecker\u6a19\u6e96\u5f62\u306e\u89e3\u6790\u3068\u30b7\u30b9\u30c6\u30e0\u5236\u5fa1\u3078\u306e\u5fdc\u7528<\/a><\/li>\n<li><a href=\"#d02\">\u975e\u7dda\u5f62\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306b\u5bfe\u3059\u308b\u7d44\u5408\u305b\u7684\u524d\u51e6\u7406\u624b\u6cd5<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#e\">\u7d71\u8a08\u7684\u30e2\u30c7\u30eb\u306e\u6700\u9069\u5316<\/a>\n<ul>\n<li><a href=\"#e01\">\u7d71\u4e00\u7684\u306a2\u5024\u5224\u5225\u30e2\u30c7\u30eb\u3068\u305d\u306e\u89e3\u6cd5\u306e\u63d0\u6848<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#b\">\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u73fe\u8c61\u306e\u89e3\u6790\u3067\u5f97\u3089\u308c\u308b\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u624b\u6cd5\u306b\u5411\u3051\u3066<\/a>\n<ul>\n<li><a href=\"#b01\">\u30c6\u30f3\u30bd\u30eb\u30c7\u30fc\u30bf\u306e\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a><\/li>\n<li><a href=\"#b02\">\u884c\u5217\u306e\u4f4e\u30e9\u30f3\u30af\u57fa\u5e95\u554f\u984c\u3068\u753b\u50cf\u5206\u96e2\u3078\u306e\u5fdc\u7528<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>&nbsp;<\/h3>\n<hr>\n<h3 id=\"c\">\u751f\u547d\u73fe\u8c61\u306e\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0<\/h3>\n<ul>\n<li>\n<h4 id=\"c02\">\u201c\u5148\u3092\u8aad\u3080\u201d\u30b3\u30a6\u30e2\u30ea\u306e\u4e09\u6b21\u5143\u98db\u884c\u7d4c\u8def\u8a08\u753b<\/h4>\n<\/li>\n<\/ul>\n<p>\u30b3\u30a6\u30e2\u30ea\u306f\u9ad8\u5ea6\u306b\u767a\u9054\u3057\u305f\u30bd\u30ca\u30fc\u30b7\u30b9\u30c6\u30e0\u3092\u7528\u3044\u3066\uff0c\u591a\u304f\u306e\u5fae\u5c0f\u306a\u98db\u7fd4\u6606\u866b\u3092\u98db\u3073\u306a\u304c\u3089\u6b21\u3005\u3068\u6355\u98df\u3059\u308b\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0c\u91ce\u5916\u5b9f\u9a13\u3068\u6570\u7406\u30e2\u30c7\u30ea\u30f3\u30b0\u306b\u3088\u3063\u3066\uff0c\u30b3\u30a6\u30e2\u30ea\u304c\u76ee\u306e\u524d\u306e\u7372\u7269\u3060\u3051\u3067\u306a\u304f\uff0c\u305d\u306e\u6b21\u306e\u7372\u7269\u306b\u8d85\u97f3\u6ce2\u30bd\u30ca\u30fc\u306b\u3088\u3063\u3066\u6ce8\u610f\u3092\u6255\u3044\uff0c\u53cc\u65b9\u306e\u7372\u7269\u3092\u9806\u6b21\u6355\u98df\u3059\u308b\u30eb\u30fc\u30c8\u3092\u98db\u884c\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u660e\u3089\u304b\u306b\u3057\u305f\uff0e\u4eca\u5f8c\uff0c\u9078\u629e\u7684\u6ce8\u610f\u6a5f\u69cb\u306b\u95a2\u3059\u308b\u7814\u7a76\u3084\uff0c\u30c9\u30ed\u30fc\u30f3\u306a\u3069\u306e\u81ea\u5f8b\u79fb\u52d5\u30ed\u30dc\u30c3\u30c8\u306e\u8ecc\u9053\u8a08\u753b\u7814\u7a76\u5206\u91ce\u306b\u304a\u3051\u308b\u65b0\u3057\u3044\u30e2\u30c7\u30eb\u52d5\u7269\u3068\u3057\u3066\u306e\u5fdc\u7528\u304c\u671f\u5f85\u3067\u304d\u308b\uff0e<\/p>\n<p>\u4ee5\u4e0b\u306e\u56f3\u306f\uff0c\u91ce\u5916\u3067\u306e\u97f3\u97ff\u8a08\u6e2c\uff08A\uff09\u3067\u5f97\u3089\u308c\u305f\u30b3\u30a6\u30e2\u30ea\u306e\u8ecc\u9053\u306e\u4e00\u4f8b\uff08B,C\uff09\u3068\uff0c\u8ecc\u9053\u30c7\u30fc\u30bf\u304b\u3089\u63a8\u5b9a\u3055\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\uff08D,E\uff09\u3067\u3042\u308b\uff0e\u6355\u98df\u6642\u9593\u9593\u9694\u304c\u9577\u3044\u3068\u304d\u306f\u76ee\u306e\u524d\u306e\u7372\u7269\uff08\u7372\u7269\uff11\uff09\u306e\u60c5\u5831\u306e\u307f\u306b\u57fa\u3065\u3044\u305f\u8ecc\u9053\u304c\u8a08\u753b\u3055\u308c\u3066\u3044\u305f\uff08D,F\uff09\u306e\u306b\u5bfe\u3057\u3066\uff0c\u6355\u98df\u6642\u9593\u9593\u9694\u304c\u77ed\u3044\u3068\u304d\u306f\u6b21\u306e\u7372\u7269\uff08\u7372\u7269\uff12\uff09\u306e\u60c5\u5831\u306b\u3082\u57fa\u3065\u3044\u3066\u8ecc\u9053\u304c\u8a08\u753b\u3055\u308c\u3066\u304a\u308a\uff08E,G\uff09\uff0c\u6355\u98df\u6210\u529f\u7387\u3092\u8abf\u3079\u305f\u6570\u5024\u8a08\u7b97\u306e\u6700\u9069\u5024\uff08D,E\u306e\u8d64\u8272\u90e8\u5206\uff09\u3068\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u306e\u30d4\u30fc\u30af\u304c\u5408\u81f4\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\uff08E\uff09\uff0e<\/p>\n<p><a href=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2015\/08\/FASAH2016s.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-303\" src=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2015\/08\/FASAH2016s.png\" alt=\"\" width=\"822\" height=\"445\"><\/a><\/p>\n<blockquote><p>&nbsp;E. Fujioka, I. Aihara, M. Sumiya, K. Aihara and S. Hiryu: Echolocating bats use future-target information for optimal foraging, <em>Proceedings of the National Academy of Sciences of the United States of America<\/em>, vol. 113, pp. 4848-4852, 2016.<\/p><\/blockquote>\n<ul>\n<li>\n<h4 id=\"c01\">\u690d\u7269\u306e\u6982\u65e5\u6642\u8a08\u306b\u5bfe\u3059\u308b\u6570\u7406\u7684\u89e3\u6790<\/h4>\n<\/li>\n<\/ul>\n<p>\u9ad8\u6b21\u5143\u306e\u6642\u7cfb\u5217\u30c7\u30fc\u30bf\u306f\u591a\u304f\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u7528\u3044\u3066\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u304c\uff0c\u91cd\u5fc3\u5ea7\u6a19\u306b\u3088\u308b\u4e88\u6e2c\u624b\u6cd5\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u5c11\u6570\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u307f\u3092\u7528\u3044\u305f\u6570\u7406\u30e2\u30c7\u30eb\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3053\u306e\u6570\u7406\u30e2\u30c7\u30eb\u306b\u57fa\u3065\u3044\u3066\u30b7\u30ed\u30a4\u30cc\u30ca\u30ba\u30ca\u306e\u6982\u65e5\u30ea\u30ba\u30e0\u3092\u89e3\u6790\u3057\uff0c\u690d\u7269\u306e\u6982\u65e5\u30ea\u30ba\u30e0\u306b\u5668\u5b98\u3054\u3068\u306e\u968e\u5c64\u6027\u304c\u3042\u308a\uff0c\u830e\u9802\u304c\u305d\u306e\u9802\u70b9\u306b\u4f4d\u7f6e\u3059\u308b\u3053\u3068\u304c\u660e\u3089\u304b\u306b\u306a\u3063\u305f\uff0e<\/p>\n<p><span style=\"color: #0000ff\">&gt;&gt;&gt; <a style=\"color: #0000ff\" href=\"https:\/\/www.cell.com\/cell\/abstract\/S0092-8674(15)01114-9\" target=\"_blank\" rel=\"noopener noreferrer\">\u8ad6\u6587\u3078\u306e\u30ea\u30f3\u30af\u306f\u3053\u3061\u3089<\/a><\/span><\/p>\n<blockquote><p>&nbsp;N. Takahashi, Y. Hirata, K. Aihara and P. Mas: A hierarchical multi-oscillator network orchestrates the Arabidopsis circadian system, <em>Cell<\/em>,<br \/>\nvol. 163, pp. 148-159, 2015.<\/p><\/blockquote>\n<h3>&nbsp;<\/h3>\n<hr>\n<h3 id=\"d\">\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0<\/h3>\n<ul>\n<li>\n<h4 id=\"d01\"><span style=\"line-height: 1.5\">Kronecker\u6a19\u6e96\u5f62\u306e\u89e3\u6790\u3068\u30b7\u30b9\u30c6\u30e0\u5236\u5fa1\u3078\u306e\u5fdc\u7528<\/span><\/h4>\n<\/li>\n<\/ul>\n<p>\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u7684\u96e3\u3057\u3055\u3092\u8868\u3059\u6307\u6a19\u3068\u3057\u3066\uff0cKronecker\u6307\u6570\u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\uff0e\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0\u3067\u306f\uff0c\u4e0e\u3048\u3089\u308c\u305f\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306b\u5bfe\u3057\u3066Kronecker\u6307\u6570\u306e\u5c0f\u3055\u3044\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u30e2\u30c7\u30eb\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u5fc5\u8981\u3068\u3055\u308c\u3066\u3044\u308b\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0cKronecker\u6307\u6570\u3068\u95a2\u4fc2\u306e\u6df1\u3044Kronecker\u6a19\u6e96\u5f62\u3092\u30de\u30c8\u30ed\u30a4\u30c9\u7406\u8ad6\u7684\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u3088\u308a\u89e3\u6790\u3057\u305f\uff0e\u3055\u3089\u306b\uff0c\u52d5\u7684\u30b7\u30b9\u30c6\u30e0\u306e\u53ef\u5236\u5fa1\u6027\u89e3\u6790\u3078\u306e\u5fdc\u7528\u3068\u3057\u3066\uff0c\u69cb\u9020\u53ef\u5236\u5fa1\u90e8\u5206\u7a7a\u9593\u306e\u6b21\u5143\u3092\u52b9\u7387\u7684\u306b\u8a08\u7b97\u3059\u308b\u624b\u6cd5\u3092\u63d0\u6848\u3057\u305f\uff0e<\/p>\n<blockquote><p>&nbsp;S. Iwata and M. Takamatsu: On the Kronecker canonical form of singular mixed matrix pencils, <em>SIAM Journal on Control and Optimization<\/em>,<br \/>\nvol. 55, pp. 2134-2150, 2017.<\/p><\/blockquote>\n<ul>\n<li>\n<h4 id=\"d02\">\u975e\u7dda\u5f62\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306b\u5bfe\u3059\u308b\u7d44\u5408\u305b\u7684\u524d\u51e6\u7406\u624b\u6cd5<\/h4>\n<\/li>\n<\/ul>\n<p>\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f (DAE) \u306e\u6570\u5024\u7684\u306a\u89e3\u304d\u306b\u304f\u3055\u306f\uff0c\u6307\u6570\u3068\u3088\u3070\u308c\u308b\u7279\u6027\u91cf\u306b\u3088\u3063\u3066\u7279\u5fb4\u3065\u3051\u3089\u308c\u308b\uff0eDAE \u306e\u6570\u5024\u89e3\u3092\u7cbe\u5ea6\u826f\u304f\u5f97\u308b\u305f\u3081\u306b\u306f\uff0c\u4e0e\u3048\u3089\u308c\u305f DAE \u3092\u4f4e\u6307\u6570\u306e DAE \u306b\u5909\u63db\u3059\u308b\u6307\u6570\u6e1b\u5c11\u304c\u524d\u51e6\u7406\u3068\u3057\u3066\u91cd\u8981\u3067\u3042\u308b\uff0e\u3057\u304b\u3057\uff0c\u73fe\u5728\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u308b Mattsson\u2013S\u00f6derlind \u306e\u6307\u6570\u6e1b\u5c11\u6cd5\uff08MS \u6cd5\uff09\u306f\uff0c\u3042\u308b\u7a2e\u306e DAE \u306b\u5bfe\u3057\u3066\u306f\u9069\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0c\u8a18\u53f7\u8a08\u7b97\u3068\u7d44\u5408\u305b\u7684\u624b\u6cd5\u3092\u878d\u5408\u3059\u308b\u3053\u3068\u3067\uff0cMS \u6cd5\u304c\u9069\u7528\u4e0d\u80fd\u306a\u975e\u7dda\u5f62 DAE \u3092\u9069\u7528\u53ef\u80fd\u306a DAE \u306b\u5909\u63db\u3059\u308b 2 \u7a2e\u985e\u306e\u524d\u51e6\u7406\u624b\u6cd5\u3092\u63d0\u6848\u3057\u305f\uff0e\u63d0\u6848\u624b\u6cd5\u3092\u5b9f\u88c5\u3057\u305f MATLAB \u30e9\u30a4\u30d6\u30e9\u30ea\u306f<a href=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/software\/\">\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2<\/a>\u306b\u3066\u516c\u958b\u4e2d\u3067\u3042\u308b\uff0e<\/p>\n<p>\u4ee5\u4e0b\u306e\u56f3\u306f\uff0c\u5e73\u9762\u4e0a\u306e\u30ed\u30dc\u30c3\u30c8\u30a2\u30fc\u30e0\u306e\u52d5\u4f5c\u3092\u8a18\u8ff0\u3059\u308b\u9ad8\u6307\u6570 DAE\uff08\u6587\u732e <a href=\"#CG1995\">[1]<\/a>&nbsp;\u304b\u3089\u5f15\u7528\uff09\u306b\u5bfe\u3059\u308b\u6570\u5024\u8a08\u7b97\u7d50\u679c\u3092\u793a\u3057\u3066\u3044\u308b\uff0e\u3053\u306e DAE \u306f MS \u6cd5\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305a\uff0c\u305d\u306e\u307e\u307e\u3067\u306f\u6570\u5024\u89e3\u306e\u8a08\u7b97\u304c\u56f0\u96e3\u3067\u3042\u308b\uff0e\u63d0\u6848\u624b\u6cd5\u3092\u7528\u3044\u3066 MS \u6cd5\u304c\u9069\u7528\u53ef\u80fd\u306a DAE \u306b\u4fee\u6b63\u3059\u308b\u3053\u3068\u3067\uff0c\u6307\u6570\u6e1b\u5c11\u3092\u7d4c\u7531\u3057\u3066\u6570\u5024\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\n<ol>\n<li id=\"CG1995\">S. L. Campbell, E. Griepentrog. Solvability of general differential algebraic equations. <em>SIAM Journal on Scientific Computing<\/em>, 16(2):257\u2013270, 1995.<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-368 size-large\" src=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2019\/12\/nonlinear_dae-1024x658.png\" alt=\"\" width=\"700\" height=\"450\" srcset=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2019\/12\/nonlinear_dae-1024x658.png 1024w, https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2019\/12\/nonlinear_dae-300x193.png 300w, https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2019\/12\/nonlinear_dae-768x494.png 768w, https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2019\/12\/nonlinear_dae.png 1400w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/p>\n<blockquote><p>T. Oki. Improved structural methods for nonlinear differential-algebraic equations via combinatorial relaxation. In <em>Proceedings of the 44th International Symposium on Symbolic and Algebraic Computation (ISSAC \u201919)<\/em>, pp. 315\u2212322, 2019.<\/p><\/blockquote>\n<hr>\n<h3 id=\"e\">\u7d71\u8a08\u7684\u30e2\u30c7\u30eb\u306e\u6700\u9069\u5316<\/h3>\n<ul>\n<li>\n<h4 id=\"e01\"><span style=\"line-height: 1.5\">\u7d71\u4e00\u7684\u306a2\u5024\u5224\u5225\u30e2\u30c7\u30eb\u3068\u305d\u306e\u89e3\u6cd5\u306e\u63d0\u6848<\/span><\/h4>\n<\/li>\n<\/ul>\n<p>2\u5024\u5224\u5225\u554f\u984c\u3068\u306f, \u4e0e\u3048\u3089\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u304c2\u3064\u306e\u30af\u30e9\u30b9\u306e\u3069\u3061\u3089\u306b\u5c5e\u3059\u308b\u306e\u304b\u3092\u4e88\u6e2c\u3059\u308b\u554f\u984c\u3067\u3042\u308b. \u305d\u306e\u4e88\u6e2c\u306b\u7528\u3044\u308b\u5224\u5225\u95a2\u6570\u306e\u5b9a\u3081\u65b9\u3092\u6700\u9069\u5316\u554f\u984c\u3068\u3057\u3066\u8a18\u8ff0\u3057\u305f\u3082\u306e\u304c2\u5024\u5224\u5225\u30e2\u30c7\u30eb\u3067\u3042\u308a, \u30b5\u30dd\u30fc\u30c8\u30d9\u30af\u30bf\u30fc\u30de\u30b7\u30f3\u3084\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u3092\u306f\u3058\u3081\u3068\u3057\u3066\u591a\u304f\u306e\u30e2\u30c7\u30eb\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u308b. \u672c\u7814\u7a76\u3067\u306f, \u69d8\u3005\u306a2\u5024\u5224\u5225\u30e2\u30c7\u30eb\u3092\u6271\u3044\u3084\u3059\u3044\u5f62\u3067\u7d71\u4e00\u7684\u306b\u5b9a\u5f0f\u5316\u3057, \u305d\u306e\u5b9a\u5f0f\u5316\u306b\u5bfe\u3057\u3066\u6c4e\u7528\u7684\u304b\u3064\u9ad8\u901f\u306a\u89e3\u6cd5\u3092\u63d0\u6848\u3057\u305f. \u6570\u5024\u5b9f\u9a13\u3067\u306f, \u5927\u898f\u6a21\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u8a08\u7b97\u6642\u9593\u306b\u95a2\u3057\u3066, \u65e2\u5b58\u624b\u6cd5\u306b\u5bfe\u3059\u308b\u63d0\u6848\u624b\u6cd5\u306e\u512a\u4f4d\u6027\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u305f. \u3053\u306e\u3088\u3046\u306b\u6c4e\u7528\u6027\u3068\u9ad8\u901f\u3055\u3092\u517c\u306d\u5099\u3048\u305f\u89e3\u6cd5\u306f, \u8907\u6570\u306e\u30e2\u30c7\u30eb\u306e\u5224\u5225\u7cbe\u5ea6\u3092\u6bd4\u8f03\u3057\u9069\u5207\u306a\u30e2\u30c7\u30eb\u3092\u9078\u629e\u3059\u308b\u4e0a\u3067\u6709\u7528\u3067\u3042\u308b.<\/p>\n<blockquote><p>&nbsp;N. Ito, A. Takeda and K.-C. Toh: A unified formulation and fast accelerated proximal gradient method for classification, <em>Journal of Machine Learning Research<\/em>, vol. 18, pp. 1-49, 2017.<\/p><\/blockquote>\n<h3>&nbsp;<\/h3>\n<hr>\n<h3 id=\"b\">\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u73fe\u8c61\u306e\u89e3\u6790\u3067\u5f97\u3089\u308c\u308b\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u624b\u6cd5\u306b\u5411\u3051\u3066<\/h3>\n<ul>\n<li>\n<h4 id=\"b01\"><span style=\"line-height: 1.5\">\u30c6\u30f3\u30bd\u30eb\u30c7\u30fc\u30bf\u306e\u5727\u7e2e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/span><\/h4>\n<\/li>\n<\/ul>\n<p>\u30c6\u30f3\u30bd\u30eb\u306eCP\u5206\u89e3\u306f\u4ea4\u4e92\u6700\u5c0f\u6b8b\u5dee\u6cd5(ALS\u6cd5)\u306b\u3088\u308a\u8fd1\u4f3c\u5206\u89e3\u3092\u6c42\u3081\u308b\u306e\u304c\u4e3b\u6d41\u3067\u3042\u308b\u304c\uff0c\u5927\u304d\u306a\u30c6\u30f3\u30bd\u30eb\u306b\u5bfe\u3057\u3066\u306f\u8a08\u7b97\u91cf\u304c\u5927\u304d\u3044\u3068\u3044\u3046\u96e3\u70b9\u304c\u3042\u308b\uff0e3\u968e\u30c6\u30f3\u30bd\u30eb\u306b\u5bfe\u3057\u3066\u306f\u5de7\u5999\u306a\u30b5\u30a4\u30ba\u524a\u6e1b\u3092\u7528\u3044\u305fASD\u6cd5\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u304c\uff0c\u52d5\u4f5c\u304c\u3084\u3084\u4e0d\u5b89\u5b9a\u3067\u3042\u308b\u3068\u3044\u3046\u6b20\u70b9\u304c\u3042\u308b\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0cALS\u306e\u5b89\u5b9a\u6027\u3068ASD\u306e\u9ad8\u901f\u6027\u3092\u517c\u306d\u5099\u3048\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0(reduced ALS\u6cd5)\u3092\u63d0\u6848\u3057\uff0c\u6570\u5024\u5b9f\u9a13\u306b\u3088\u308a\u6709\u7528\u6027\u3092\u793a\u3057\u305f\uff0e<\/p>\n<p>\u4ee5\u4e0b\u306e\u56f3\u306f\uff0c\u3042\u308b\u7537\u6027\u306e\u9854\u5199\u771f\u309210\u679a\u4e26\u3079\u305f\u30c7\u30fc\u30bf\u3092CP\u5206\u89e3\u306b\u3088\u308a\u5727\u7e2e\u3057\u305f\u3082\u306e\u3067\u3042\u308b\uff0eReduced ALS\u6cd5\u306f\u5143\u306e\u753b\u50cf\u3092\u3042\u308b\u7a0b\u5ea6\u4fdd\u6301\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\uff0e<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-199\" src=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2015\/08\/pic2.png\" alt=\"Reduced ALS\u6cd5\" width=\"500\" border=\"1\"><\/p>\n<blockquote><p>&nbsp;T. Murakoshi and T. Matsuo: A fast alternating least squares method for third-order tensors based on a compression procedure, <em>JSIAM Letters<\/em>, vol. 7, pp. 5-8, 2015.<\/p><\/blockquote>\n<ul>\n<li>\n<h4 id=\"b02\"><span style=\"line-height: 1.5\">\u884c\u5217\u306e\u4f4e\u30e9\u30f3\u30af\u57fa\u5e95\u554f\u984c\u3068\u753b\u50cf\u5206\u96e2\u3078\u306e\u5fdc\u7528<\/span><\/h4>\n<\/li>\n<\/ul>\n<p>\u30d9\u30af\u30c8\u30eb\u30fb\u884c\u5217\u306b\u304a\u3051\u308b\u300c\u758e\u30fb\u4f4e\u30e9\u30f3\u30af\u300d\u306a\u8868\u73fe\u306f\u30c7\u30fc\u30bf\u5727\u7e2e\u306b\u6709\u7528\u3067\u3042\u308b\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0c\u884c\u5217\u306e\u4f4e\u30e9\u30f3\u30af\u57fa\u5e95\u3092\u6c42\u3081\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u6848\u3057\uff0c\u672c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u753b\u50cf\u5206\u96e2\u3078\u306e\u5fdc\u7528\u3092\u793a\u3057\u305f\uff0e<\/p>\n<p>\u4ee5\u4e0b\u306e\u56f3\u306f\uff0c4\u679a\u306e\u753b\u50cf\u3092\u4f4e\u30e9\u30f3\u30af\u884c\u5217\u3067\u8fd1\u4f3c\u3057\u6df7\u5408\u3057\u3066\u304b\u3089\uff0c\u672c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u7528\u3044\u3066\u5206\u96e2\u3057\u305f\u3082\u306e\u3067\u3042\u308b\uff0e\u6df7\u3056\u3063\u305f\u753b\u50cf\u304c\u6b63\u3057\u304f\u5206\u96e2\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u308b\uff0e<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-medium wp-image-200\" src=\"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-content\/uploads\/sites\/2\/2015\/08\/pic3.png\" alt=\"\u884c\u5217\u306e\u4f4e\u30e9\u30f3\u30af\u57fa\u5e95\u554f\u984c\" width=\"500\" border=\"1\"><\/p>\n<blockquote><p>Y. Nakatsukasa, T. Soma and A. Uschmajew: Finding a low-rank basis in a matrix subspace, <em>Mathematical Programming Series A<\/em>, 2016.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\u751f\u547d\u73fe\u8c61\u306e\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0 \u201c\u5148\u3092\u8aad\u3080\u201d\u30b3\u30a6\u30e2\u30ea\u306e\u4e09\u6b21\u5143\u98db\u884c\u7d4c\u8def\u8a08\u753b \u690d\u7269\u306e\u6982\u65e5\u6642\u8a08\u306b\u5bfe\u3059\u308b\u6570\u7406\u7684\u89e3\u6790&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-48","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/pages\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/comments?post=48"}],"version-history":[{"count":8,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/pages\/48\/revisions"}],"predecessor-version":[{"id":394,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/pages\/48\/revisions\/394"}],"wp:attachment":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/media?parent=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}