{"id":2113,"date":"2014-10-12T21:11:15","date_gmt":"2014-10-12T12:11:15","guid":{"rendered":"http:\/\/na-inet.jp\/weblog2\/?p=2113"},"modified":"2014-10-12T21:22:11","modified_gmt":"2014-10-12T12:22:11","slug":"fast-matrix-multiplication-is-stable-but","status":"publish","type":"post","link":"https:\/\/na-inet.jp\/weblog2\/2014\/10\/12\/fast-matrix-multiplication-is-stable-but\/","title":{"rendered":"&#8220;Fast matrix multiplication is stable,&#8221; but&#8230;"},"content":{"rendered":"<p>\u3000\u4eca\u5e74(2014\u5e74)\u306e3\u6708\u306b\u5fdc\u7528\u6570\u7406\u5b66\u4f1a\u9023\u5408\u7814\u7a76\u4f1a\u3067\u591a\u500d\u9577<a href=\"http:\/\/en.wikipedia.org\/wiki\/Strassen_algorithm\" target=\"_blank\">Strassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a>\u306b\u3064\u3044\u3066\u558b\u3063\u305f\u6642\u306b\uff0c&#8221;Group-theoretic\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0&#8221;\u306e\u8a71\u304c\u3061\u3087\u308d\u3063\u3068\u51fa\u305f\u306e\u3067\uff0cStrassen\u306e\u4ef6\u304c\u843d\u3061\u7740\u3044\u305f\u6642\u306b\u3061\u3087\u3063\u3068\u8abf\u3079\u3066\u307f\u305f\u306e\u3067\u3042\u308b\u3002\u30fb\u30fb\u30fb\u306a\u308b\u307b\u3069\u78ba\u304b\u306b\u300c\u4e00\u6642\u306f\u300d\u76db\u308a\u4e0a\u304c\u3063\u3066\u3044\u305f\u3088\u3046\u3060\u304c\uff0c\u5b9f\u88c5\u306b\u7d61\u3080\u5927\u4e8b\u306a\u8ad6\u6587\u304c\u6d88\u3048\u3066\u3057\u307e\u3063\u3066\u4ee5\u6765\uff0c\u3069\u30fc\u3082\u6700\u8fd1\u96f2\u884c\u304d\u304c\u602a\u3057\u3044\u3088\u3046\u306a\u306e\u3067\u3042\u308b\u3002\u3068\u306f\u3044\u3048\uff0c\u9762\u767d\u305d\u3046\u306a\u8a71\u984c\u3067\u306f\u3042\u308b\u3057\uff0c\u3061\u3087\u3063\u3068\u305a\u3064\u52c9\u5f37\u3057\u3066\u3044\u304f\u306b\u306f\u826f\u3055\u305d\u3046\u306a\u3082\u306e\u306a\u306e\u3067\uff0c\u30b3\u30e1\u30f3\u30c8\u3044\u305f\u3060\u3044\u305f\u65b9\u306b\u5bfe\u3057\u3066\u300c\u4e00\u5fdc\u306f\u8abf\u3079\u3066\u307f\u307e\u3057\u305f\u3088\u300d\u3068\u3044\u3046\u5831\u544a\u304c\u3066\u3089\uff0c\u3053\u306e\u8a18\u4e8b\u3092\u8d77\u3053\u3057\u305f\u3068\u3044\u3046\u6b21\u7b2c\u3067\u3042\u308b\u3002\u300c\u5b9f\u88c5\u306b\u7d61\u3080\u5927\u4e8b\u306a\u8ad6\u6587\u300d\u306e\u305d\u306e\u5f8c\u3084&#8221;Group-Theoretic\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0&#8221;\u306e\u52d5\u5411\u3092\u3054\u5b58\u77e5\u306e\u65b9\u304c\u3044\u3089\u3063\u3057\u3083\u3063\u305f\u3089\u60c5\u5831\u3082\u9802\u3051\u308b\u3068\u5e78\u3044\u3067\u3042\u308b\u3002<\/p>\n<p>\u3000\u3064\u30fc\u3053\u3068\u3067<a href=\"http:\/\/jsiaml.jsiam.org\/jsiaml_Announcement-ja.html\" target=\"_blank\">\u591a\u500d\u9577Strassen\u306e\u8ad6\u6587\u63b2\u8f09\u304c\u6c7a\u307e\u3063\u305f<\/a>\u306e\u3067\uff0c<a href=\"file:\/\/\/C:\/Users\/tkouya\/Documents\/websites\/na-inet.jp\/na\/bnc\/bncmatmul-0.1.tar.bz2\" target=\"_blank\">\u30bd\u30fc\u30b9\u3082\u5916\u306b\u51fa\u3057\u305f<\/a>\u3002\u308d\u304f\u3059\u3063\u307d\u6574\u7406\u3057\u3066\u306a\u3044\u4ee3\u7269\u306a\u306e\u3060\u304c\uff0c\u3061\u3087\u308d\u3063\u3068\u5f15\u304d\u5408\u3044\u3082\u3042\u3063\u305f\u3053\u3068\u3082\u3042\u3063\u3066\uff0c\u3061\u3083\u3093\u3068\u52d5\u3044\u3066\u3044\u308b\u3068\u3044\u3046\u8a3c\u62e0\u7269\u4ef6\u306a\u306e\u3067\u65e9\u3081\u306b\u51fa\u3059\u3053\u3068\u306b\u3057\u305f\u306e\u3067\u3042\u308b\u3002<br \/>\n\u3000\u3061\u306a\u307f\u306b\u3053\u308c\uff0c\u6bd4\u8f03\u5bfe\u8c61\u306e\u305f\u3081\u500d\u7cbe\u5ea6\u306e\u884c\u5217\u7a4d\u3082Intel Math Kernel(IMKL)\u63d0\u4f9bdgemm\u95a2\u6570\u3092\u5229\u7528\u3057\u3066\u5b9f\u88c5\u3057\u3066\u304a\u308a\uff0c\u305d\u306e\u7d50\u679c\u306b\u3064\u3044\u3066\u306f<a href=\"http:\/\/na-inet.jp\/research\/kiyo14.pdf\" target=\"_blank\">\u7d00\u8981\u539f\u7a3f<\/a>\u306b\u66f8\u3044\u3066\u3042\u308b\u3002\u307e\uff0c\u30e1\u30a4\u30f3\u306f\u591a\u500d\u9577\u884c\u5217\u7a4d\u306e\u65b9\u306a\u306e\u3067\uff0c\u3042\u304f\u307e\u3067\u6bd4\u8f03\u7528\u306a\u306e\u3060\u304c\uff0c\u5b58\u5916\u5b9f\u88c5\u304c\u96e3\u3057\u3044\u306a\u3041\u3068\u3044\u3046\u611f\u60f3\u3092\u6301\u3063\u305f\u3002\u7279\u306b2^n\u3067\u306a\u3044\u884c\u6570\u30fb\u5217\u6570\u306e\u6642\u306e\u51e6\u7406\u304c\u5927\u5909\u3067\uff0c\u4eca\u306e\u3068\u3053\u308d\u306f\u591a\u500d\u9577\u306b\u5408\u308f\u305b\u3066\u30d1\u30c7\u30a3\u30f3\u30b0\uff080\u8981\u7d20\u3092\u8a70\u3081\u8fbc\u3093\u30672^n\u306e\u500d\u6570\u306e\u884c\u6570\u30fb\u5217\u6570\u306b\u3059\u308b)\u3068\u30d4\u30fc\u30ea\u30f3\u30b0(2^n\u306e\u500d\u6570\u3092\u306f\u307f\u51fa\u308b\u90e8\u5206\u306f\u30d6\u30ed\u30c3\u30af\u5316\u3057\u3066\u5225\u306b\u51e6\u7406\u3059\u308b\uff09\u51e6\u7406\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u5b9f\u88c5\u3057\u3066\u3044\u308b\u304c\uff0c<a href=\"http:\/\/ci.nii.ac.jp\/naid\/110009536431\" target=\"_blank\">ATLAS\u30d9\u30fc\u30b9\u306eStrassen\u5b9f\u88c5\u5831\u544a<\/a>\u306b\u3042\u308b\u901a\u308a\uff0c\u500d\u7cbe\u5ea6\u3050\u3089\u3044\u3060\u3068\u30d1\u30c7\u30a3\u30f3\u30b0\u3060\u3051\u3067\u30b5\u30a4\u30ba\u5408\u308f\u305b\u3092\u3057\u305f\u65b9\u304c\u7121\u96e3\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3061\u306a\u307f\u306b\u5965\u6751\u5148\u751f\u306e\u300c<a href=\"https:\/\/oku.edu.mie-u.ac.jp\/~okumura\/algo\/\" target=\"_blank\">C\u8a00\u8a9e\u306b\u3088\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u4e8b\u5178<\/a>\u300d\u300c<a href=\"https:\/\/oku.edu.mie-u.ac.jp\/~okumura\/java-algo\/\" target=\"_blank\">Java\u306b\u3088\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u4e8b\u5178<\/a>\u300d\u306b\u3082Strassen\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a71\u984c\u304c\u3042\u308b\u304c\uff0c<a href=\"http:\/\/www.davidhbailey.com\/dhbpapers\/mxm.pdf\" target=\"_blank\">1988\u5e74\u306eBailey\u8ad6\u6587<\/a>\u3067\u306e\u6210\u679c\u3092\u5143\u306b\u3057\u3066\u3044\u308b\u300c2048\u00d72048\u306e\u884c\u5217\u7a4d\u30675\u5272\u9ad8\u901f\u300d\u3068\u3044\u3046\u8a18\u8ff0\u3092\u305d\u306e\u307e\u307e\u771f\u306b\u53d7\u3051\u308b\u3068\u30d0\u30ab\u3092\u898b\u308b\uff0c\u3068\u3044\u3046\u3053\u3068\u306fATLAS\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5\u3068\u30ef\u30b7\u306e\u3084\u3063\u305fIMKL\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5\uff0c\u4e21\u65b9\u306e\u7d50\u679c\u3092\u898b\u3066\u3082\u3089\u3048\u3070\u3054\u7406\u89e3\u3044\u305f\u3060\u3051\u308b\u3060\u308d\u3046\u3002\u73fe\u5728\u307e\u3067\u306eStrassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30b5\u30fc\u30d9\u30a4\u306b\u3064\u3044\u3066\u306f\u30ef\u30b7\u306e\u7d00\u8981\u539f\u7a3f\u306b\u3082\u3061\u3089\u3068\u66f8\u3044\u305f\u304c\uff0c<a href=\"http:\/\/www.maths.manchester.ac.uk\/~higham\/asna\/\" target=\"_blank\">\u30b9\u30dd\u30c3\u30af\u535a\u58eb\u306e\u5206\u539a\u3044\u672c<\/a>\u306e23\u7ae0\u304c\u4e00\u756a\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u307e\u3068\u307e\u3063\u3066\u3044\u308b\u306e\u3067\u53c2\u7167\u3055\u308c\u305f\u3044\u3002<\/p>\n<p>\u3000\u3064\u307e\u308a\u500d\u7cbe\u5ea6\u8a08\u7b97\u3060\u3068\uff0c\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387\u30fbSIMD\u547d\u4ee4\u306e\u6d3b\u7528\u30fb\u30e1\u30e2\u30ea\u64cd\u4f5c\u95a2\u6570\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306b\u3088\u308b\u5f71\u97ff\u304c\u5927\u304d\u304f\u51e6\u7406\u6642\u9593\u306b\u4f5c\u7528\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u306e\u3067\uff0c\u6f14\u7b97\u91cf\u3092\u591a\u5c11\u6e1b\u3089\u3057\u305f\u3068\u3053\u308d\u3067\uff0cStrassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u3068\u306a\u308b\u524d\u51e6\u7406\u30fb\u5f8c\u51e6\u7406\u3092\u3082\u542b\u3081\u308b\u3068\uff0c\u5168\u4f53\u3068\u3057\u3066\u51e6\u7406\u6642\u9593\u304c\u6e1b\u3089\u305b\u308b\u304b\u3069\u3046\u304b\u306f\u3084\u3063\u3066\u307f\u306a\u3044\u3068\u3088\u304f\u5206\u304b\u3089\u306a\u3044\u3068\u3053\u308d\u304c\u5927\u304d\u3044\u306e\u3067\u3042\u308b\u3002\u305d\u306e\u70b9\uff0c\u5143\u3005\u56db\u5247\u6f14\u7b97\u306e\u51e6\u7406\u901f\u5ea6\u304c\u30c8\u30ed\u3044\u591a\u500d\u9577\u8a08\u7b97\u3060\u3068\uff0c\u6f14\u7b97\u91cf\u306e\u6e1b\u5c11\u304c\u30c0\u30a4\u30ec\u30af\u30c8\u306b\u51e6\u7406\u6642\u9593\u306e\u6e1b\u5c11\u306b\u7e4b\u304c\u308b\u306e\u3067\u5927\u5909\u5206\u304b\u308a\u3084\u3059\u3044\u7d50\u679c\u306b\u306a\u308b\u3002\u3064\u30fc\u3053\u3068\u3067\u4efb\u610f\u30b5\u30a4\u30ba\u306e\u884c\u5217\u7a4d\u306e\u8a08\u7b97\u304cStrassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u53ef\u80fd\u306b\u306a\u308c\u3070\uff0cLU\u5206\u89e3\u306e\u51e6\u7406\u6642\u9593\u3082\u6700\u59273\u5272\u6e1b\u3068\u306a\u308b\u306e\u3067\u3042\u308b\u3002\u9006\u306b\u8a00\u3048\u3070\uff0c\u4eca\u6642\u500d\u7cbe\u5ea6\u8a08\u7b97\u3067LU\u5206\u89e3\u306b\u9069\u7528\u3057\u3066\u3082\uff0cPC\u5358\u4f53\u306e\u30aa\u30f3\u30e1\u30e2\u30ea\u3067\u53ce\u307e\u308b\u30b5\u30a4\u30ba\u306e\u554f\u984c\u7a0b\u5ea6\u3067\u306f\u6b86\u3069\u52b9\u679c\u306f\u306a\u3044\u306e\u3067\u306f\uff0c\u3068\u601d\u3048\u308b\u306e\u3067\u3042\u308b\u3002Bailey\u5148\u751f\u306eCray-2\u3068\u4eca\u306ex86\u74b0\u5883\u3068\u3067\u306f\uff0c\u30ad\u30e3\u30c3\u30b7\u30e5\u3084SIMD\u547d\u4ee4\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u305f\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u3082\u5927\u5206\u7570\u306a\u3063\u3066\u3044\u308b\u306e\u3067\uff0c\u540c\u4e00\u8996\u3057\u3066\u306f\u3044\u304b\u3093\u306e\u3067\u3042\u308b\u3002<\/p>\n<p>\u3000\u305d\u3093\u3060\u3051\uff0c\u4eca\u306e\u8a08\u7b97\u74b0\u5883\u3067\u306f\u9ad8\u901f\u3060\u304c\u524d\u51e6\u7406\u30fb\u5f8c\u51e6\u7406\u306e\u8907\u96d1\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5\u306f\u8077\u4eba\u82b8\u304c\u5fc5\u8981\u3067\u3042\u308a\uff0c\u307e\u3057\u3066\u3084Strassen\u3084Winograd\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3088\u308a\u3082\u8907\u96d1\u602a\u5947\u306a&#8221;Group-Theoretic \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0&#8221;\u3063\u3066\u5974\u306e\u5b9f\u88c5\u306f\u76f8\u5f53\u306a\u56f0\u96e3\u304c\u4e88\u60f3\u3055\u308c\u308b\u3002\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u30aa\u30ea\u30b8\u30ca\u30eb\u304c<a href=\"http:\/\/users.cms.caltech.edu\/~umans\/papers\/CKSU05.pdf\" target=\"_blank\">\u3053\u308c<\/a>\u3067\uff0c\u305d\u308c\u306b\u5bfe\u3057\u3066\u8aa4\u5dee\u89e3\u6790\u306e\u89b3\u70b9\u304b\u3089&#8221;Stable&#8221;\u3068\u3044\u3046\u5224\u5b9a\u3092\u4e0b\u3057\u305f\uff08\u30a4\u30de\u30a4\u30c1\u7591\u554f\u304c\u3042\u308b\u306e\u3060\u304c\uff09\u8ad6\u6587\u304c<a href=\"http:\/\/arxiv.org\/abs\/math\/0603207\" target=\"_blank\">\u3053\u308c<\/a>\u3067\u3042\u308b\u3089\u3057\u3044\u3002\u5f8c\u8005\u306b\u3064\u3044\u3066\u306f\u67fb\u8aad\u8ad6\u6587\u306b\u306a\u3063\u3066\u3044\u308b\u3088\u3046\u306a\u306e\u3067\uff08<a href=\"http:\/\/link.springer.com\/article\/10.1007%2Fs00211-007-0061-6#page-1\" target=\"_blank\">\u3053\u308c<\/a>\uff09\uff0c\u5185\u5bb9\u7684\u306b\u3069\u3046\u3053\u3046\u3044\u3046\u6c17\u306f\u306a\u3044\u306e\u3060\u304c\uff0c\u554f\u984c\u306f\u5f8c\u8005\u306e\u5974\u306b\u3042\u308b\u53c2\u8003\u6587\u732e[8]\u3002\u3069\u3046\u3084\u3089\u5b9f\u88c5\u3057\u305f\u7d50\u679c\u306b\u3064\u3044\u3066\u306e\u5831\u544a\u3089\u3057\u3044\u306e\u3060\u304c\uff0c\u691c\u7d22\u3057\u3066\u3082\u898b\u3064\u304b\u3089\u306a\u3044\u3057\uff0c\u540c\u69d8\u306b\u5b9f\u88c5\u3057\u305f\u7d50\u679c\u306b\u3064\u3044\u3066\u8a18\u8ff0\u3057\u305f\u3082\u306e\u304c\u4e00\u3064\u3082\u898b\u3064\u304b\u3089\u306a\u3044\u306e\u3067\u3042\u308b\u3002\u3069\u306a\u305f\u304b\u30c1\u30e3\u30ec\u30f3\u30b8\u3057\u3066\u5931\u6557\u3057\u305f\u3063\u3066\u8a18\u8ff0\u3067\u3082\u3042\u308b\u306a\u3089\u5206\u304b\u308b\u3093\u3060\u304c\uff0c\u3069\u30fc\u3082\u4eca\u306e\u3068\u3053\u308d\u3061\u3083\u3093\u3068\u5b9f\u88c5\u3057\u305f\u4eba\u304c\u4e00\u4eba\u3082\u3044\u306a\u3044\u3093\u3058\u3083\u306a\u3044\u306e\u304b\u3068\u30ef\u30b7\u306f\u5927\u3044\u306b\u7591\u3063\u3066\u3044\u308b\u306e\u3067\u3042\u308b\u3002\u53c2\u8003\u6587\u732e[8]\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u306e\u306f\u5b9f\u88c5\u306b\u5931\u6557\u3057\u305f\u304b\uff0c\u4f5c\u3063\u3066\u307f\u305f\u3051\u3069\u500d\u7cbe\u5ea6\u7a0b\u5ea6\u3067\u306f\u9ad8\u901f\u306b\u3067\u304d\u306a\u304b\u3063\u305f\u3093\u3058\u3083\u306a\u3044\u306e\u304b\u306a\uff5e\uff0c\u3068\u4eca\u306e\u3068\u3053\u308d\u8003\u3048\u3066\u3044\u308b\u3002\u307e\uff0cStrassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7d50\u679c\u3092\u898b\u308b\u9650\u308a\u7121\u7406\u3082\u306a\u3044\u304b\u306a\u3041\u3068\u306f\u601d\u3046\u306e\u3067\u3042\u308b\u3002\u524d\u51e6\u7406\u3068\u5f8c\u51e6\u7406\u306b\u3081\u3093\u3069\u304f\u3055\u305d\u3046\u306aFFT?\u3092\u4f7f\u3063\u3066\u3044\u3088\u3046\u3060\u304b\u3089\uff0c\u304b\u306a\u308a\u96e3\u3057\u3044\u3093\u3058\u3083\u306a\u3044\u306e\u304b\u3057\u3089\u3093\uff1f\u3000\u307e\u3041\u3060\u304b\u3089\u3053\u305d\u300c\u591a\u500d\u9577\u3067\u3084\u3063\u3066\u307f\u305f\u3089\u3044\u3044\u306e\u3067\u306f\u300d\u3068\u3044\u3046\u3054\u610f\u898b\u3082\u5206\u304b\u308b\u3093\u3060\u3051\u3069\uff0c\u3055\u30fc\u3066\u30fb\u30fb\u30fb\uff1f<\/p>\n<p>\u3000\u3068\uff0c\u3053\u306e\u5148\u306f\u30ef\u30b7\u304c\u8003\u3048\u3066\u3044\u3051\u3070\u6e08\u3080\u3053\u3068\u306a\u306e\u3067\uff0c\u5c11\u3057\u6642\u9593\u3092\u304b\u3051\u3066\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u89e3\u8aad\u3057\u3066\u307f\u308b\u304c\uff0c\u4f55\u5206\uff0c\u304b\u306a\u308a\u6d6e\u4e16\u96e2\u308c\u3057\u305f\u611f\u306e\u3042\u308b\u7814\u7a76\u30c6\u30fc\u30de\u3060\u3057\uff0c\u305d\u306e\u5f8c\u306e\u9032\u5c55\u304c\u805e\u304b\u308c\u306a\u3044\u3068\u3053\u308d\u3092\u898b\u308b\u3068\uff0c\u3044\u308d\u3044\u308d\u5b9f\u88c5\u4e0a\u306e\u56f0\u96e3\u3082\u3042\u308a\u305d\u3046\u3067\u3042\u308b\u3002\u3060\u304b\u3089\u3053\u305d\u306e\u30c1\u30e3\u30ec\u30f3\u30b8\u30f3\u30b0\u306a\u30c6\u30fc\u30de\u3068\u3082\u8a00\u3048\u308b\u3051\u3069\uff0c\u305d\u3046\u3044\u3046\u306e\u306f\u3082\u3063\u3068\u982d\u306e\u3044\u3044\u4eba\u306b\u53d6\u308a\u7d44\u3093\u3067\u3082\u3089\u3048\u306a\u3044\u304b\u306a\u3041\u3068\u601d\u3063\u3066\u3044\u308b\u306e\u3067\u3042\u308b\u3002\u3082\u3057\u3069\u306a\u305f\u304b\u65e2\u306b\u7740\u624b\u3055\u308c\u3066\u305d\u308c\u306a\u308a\u306e\u6210\u679c\u304c\u51fa\u3066\u3044\u308b\u3088\u3046\u3067\u3057\u305f\u3089\uff0c\u304a\u77e5\u3089\u305b\u9802\u3051\u308c\u3070\u5e78\u3044\u306a\u306e\u3067\u3042\u308b\u3002\u3042\uff0c\u9ed9\u3063\u3066\u3044\u3066\u304f\u308c\u3068\u8a00\u308f\u308c\u308c\u3070\u9ed9\u3063\u3066\u307e\u3059\u306e\u3067\u3053\u3063\u305d\u308a\u3067\u3082\u7d50\u69cb\u3067\u3054\u3056\u3044\u307e\u3059\uff0c\u306f\u3044\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u4eca\u5e74(2014\u5e74)\u306e3\u6708\u306b\u5fdc\u7528\u6570\u7406\u5b66\u4f1a\u9023\u5408\u7814\u7a76\u4f1a\u3067\u591a\u500d\u9577Strassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u558b\u3063\u305f\u6642\u306b\uff0c&#8221;Group-theoretic\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0&#8221;\u306e\u8a71\u304c\u3061\u3087\u308d\u3063\u3068\u51fa\u305f\u306e\u3067\uff0cStrassen\u306e &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/na-inet.jp\/weblog2\/2014\/10\/12\/fast-matrix-multiplication-is-stable-but\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;&#8220;Fast matrix multiplication is stable,&#8221; but&#8230;&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[7],"tags":[],"class_list":["post-2113","post","type-post","status-publish","format-standard","hentry","category-7"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/posts\/2113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/comments?post=2113"}],"version-history":[{"count":9,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/posts\/2113\/revisions"}],"predecessor-version":[{"id":2122,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/posts\/2113\/revisions\/2122"}],"wp:attachment":[{"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/media?parent=2113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/categories?post=2113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/tags?post=2113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}