\n\u6211\u3005\u306f\u3053\u308c\u307e\u3067\u306b\uff0c\u5e2f\u884c\u5217 reduction \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u3082\u3068\u306b\u3057\u305f\uff0c\u3042\u308b\u7a2e\u306e\u758e\u69cb\u9020\u3092\u3082\u3064\u5b9f\u5bfe\u79f0\u758e\u884c\u5217\u306b\u5bfe\u3059\u308b\u52b9\u7387\u7684\u306a\u4e09\u91cd\u5bfe\u89d2\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u6848\u3057\u305f\uff0e\u672c\u767a\u8868\u3067\u306f\uff0c\u672c\u758e\u884c\u5217\u4e09\u91cd\u5bfe\u89d2\u5316\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5bfe\u3059\u308b\u524d\u51e6\u7406\u3068\u3057\u3066\u884c\u5217\u306e\u884c\u30fb\u5217\u3092\u7f6e\u63db\u3059\u308b\u51e6\u7406\uff08\u30aa\u30fc\u30c0\u30ea\u30f3\u30b0\uff09\u3092\u9069\u7528\u3057\u305f\u7d50\u679c\u306b\u3064\u3044\u3066\u5831\u544a\u3059\u308b\uff0e\n<\/div>\n
6\u89d2\u5f62\u9396\u72b6\u9023\u7d50\u6709\u5411\u30b0\u30e9\u30d5\u306e\u56fa\u6709\u5024\u3068\u305d\u306e\u5fdc\u7528<\/span>
\n\u25cb\u67cf\u539f\u85cd\uff08\u6771\u4eac\u9ad8\u5c02\uff09\uff0c\u5357\u51fa\u5927\u6a39\uff08\u6771\u4eac\u9ad8\u5c02\uff09<\/span><\/p>\n\n\u5316\u5b66\u3067\u306f\uff0c\u7269\u8cea\u306e\u82b3\u9999\u65cf\u6027\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306bNICS\u3068\u3044\u3046\u5024\u304c\u7528\u3044\u3089\u308c\u3066\u3044\u308b\uff0e\u3057\u304b\u3057\uff0c\u96fb\u5b50\u304c\u5897\u3048\u308b\u306b\u3064\u308c\u3066\u305d\u306e\u8a08\u7b97\u306f\u975e\u5e38\u306b\u56f0\u96e3\u306b\u306a\u308b\u305f\u3081\uff0c\u8fd1\u4f3c\u5024\u306b\u95a2\u3059\u308b\u7814\u7a76\u304c\u884c\u308f\u308c\u3066\u3044\u308b\uff0e\u4f8b\u3048\u3070\uff0c\u30d9\u30f3\u30bc\u30f3\u74b0\u3092\u4e00\u76f4\u7dda\u72b6\u306b\u7e2e\u5408\u3055\u305b\u305f\u30dd\u30ea\u30a2\u30bb\u30f3\u306b\u95a2\u3057\u3066\u306f\uff0c\u8d8a\u9ad8\u3068\u4e95\u624b\u306b\u3088\u308a\u6709\u5411\u30b0\u30e9\u30d5\u306e\u56fa\u6709\u5024\u3092\u7528\u3044\u305f\u5024\u304c\u63d0\u6848\u3055\u308c\u305f\uff0e\u672c\u7814\u7a76\u3067\u306f\uff0c\u8d8a\u9ad8\u306e\u4e88\u60f3\u3092\u3082\u3068\u306b\uff0c\u4e00\u822c\u306e\u74b0\u6570\u3092\u6301\u30646\u89d2\u5f62\u9396\u72b6\u9023\u7d50\u6709\u5411\u30b0\u30e9\u30d5\u306e\u96a3\u63a5\u884c\u5217\u306e\u56fa\u6709\u5024\u304ccos\u3092\u7528\u3044\u305f\u5358\u7d14\u306a\u5f0f\u3067\u660e\u793a\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\n<\/div>\n
\u3042\u308b\u975e\u5bfe\u79f0\u884c\u5217\u306e\u6442\u52d5\u3092\u53d7\u3051\u305f\u5bfe\u89d2\u884c\u5217\u306e\u96e2\u6563\u53ca\u3073\u30a2\u30ca\u30ed\u30b0\u56fa\u6709\u5024\u8a08\u7b97<\/span>
\n\u25cb\u5409\u6fa4\u771f\u592a\u90ce\uff08\u30c8\u30e8\u30bf\u81ea\u52d5\u8eca\u682a\u5f0f\u4f1a\u793e\uff09<\/span><\/p>\n\n\u7b2c30\u56de\u5358\u72ec\u7814\u7a76\u4f1a\u5831\u544a\u306e\u9032\u5c55\uff0e\u6b63\u5b9a\u5024\u5bfe\u89d2\u884c\u5217\u3092\uff24, \u5b9f\u5217\u30d9\u30af\u30c8\u30eb\u3092\uff58,y\u3068\u3057\u305f\u3068\u304d, \uff24\uff0bxy^T\u306a\u3069\u306e\u884c\u5217\u306e\u56fa\u6709\u5024\u53ca\u3073\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u540c\u6642\u306b\u6c42\u3081\u308b\u554f\u984c\u3092\u5236\u7d04\u7121\u3057\u306e\u6700\u9069\u5316\u554f\u984c\u3068\u3057\u3066\u5b9a\u5f0f\u5316\u3057,\u305d\u306e\u9023\u7d9a\u7684\u53ca\u3073\u96e2\u6563\u7684\u89e3\u6cd5\u306b\u3064\u3044\u3066\u8003\u6848\u3057\u305f\uff0e\u524d\u56de\u306e\u5831\u544a\u7d50\u679c\u306f\u53b3\u5bc6\u89e3\u306b\u6f38\u8fd1\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u306a\u304b\u3063\u305f\u304c\uff0c\u3053\u306e\u90e8\u5206\u3092\u6539\u826f\u3057\u305f\uff0e\n<\/div>\n
\u6442\u52d5\u6210\u5206\u3092\u9650\u5b9a\u3059\u308b\u5168\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u306b\u5bfe\u3059\u308b\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3068\u6570\u5024\u89e3\u6cd5\u306e\u6f38\u8fd1\u89e3\u6790<\/span>
\n\u25cb\u76f8\u5cf6\u5065\u52a9\uff08\u6cd5\u653f\u5927\u5b66\u60c5\u5831\u79d1\u5b66\u90e8\uff09<\/span><\/p>\n\n\u5168\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u306f\uff0c\u89b3\u6e2c\u306b\u5bfe\u5fdc\u3059\u308b\u884c\u5217\u30c7\u30fc\u30bf\u304c\u8aa4\u5dee\u3092\u542b\u3080\u5834\u5408\uff0c\u5177\u4f53\u7684\u306b\u306f\u7d71\u8a08\u3084\u4fe1\u53f7\u51e6\u7406\u7b49\u3067\u3088\u304f\u73fe\u308c\u308b\uff0e\u89b3\u6e2c\u306e\u969b\u306b\uff0c\u7279\u5b9a\u306e\u884c\u5217\u6210\u5206\u306b\u304a\u3044\u3066\u306f\uff0c\u8aa4\u5dee\u306e\u7121\u3044\u4fe1\u983c\u3067\u304d\u308b\u6210\u5206\u3068\u898b\u306a\u305b\u308b\u5834\u5408\u304c\u3042\u308a\uff0c\u3053\u308c\u306f\u7279\u6b8a\u306a\u5168\u6700\u5c0f\u4e8c\u4e57\u554f\u984c\u306b\u5e30\u7740\u3057\uff0c\u7279\u7570\u5024\u5206\u89e3\u306b\u3088\u308a\u89e3\u3051\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\uff0e\u305f\u3060\u3057\uff0c\u3053\u306e\u5834\u5408\u306e\u6442\u52d5\u306e\u7d71\u8a08\u30e2\u30c7\u30eb\u306f\u4e00\u5207\u691c\u8a0e\u3055\u308c\u3066\u3044\u306a\u3044\u3088\u3046\u3067\u3042\u308b\uff0e\u672c\u767a\u8868\u3067\u306f\uff0c\u6442\u52d5\u306b\u5bfe\u3059\u308b\u81ea\u7136\u306a\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u3092\u884c\u3044\uff0c\u6570\u5024\u89e3\u6cd5\u3067\u5f97\u3089\u308c\u308b\u90e8\u5206\u7a7a\u9593\u304c\u63a8\u5b9a\u91cf\u3068\u3057\u3066\u306e\u4e00\u81f4\u6027\u3092\u6709\u3059\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\n<\/div>\n
\u884c\u5217\u30fb\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5\u3068\u305d\u306e\u5fdc\u7528(2)\u3000\uff0811:10 – 12:30\uff09\u3000\u5ea7\u9577\uff1a\u76f8\u5cf6 \u5065\u52a9\uff08\u6cd5\u653f\u5927\u5b66\uff09<\/strong><\/p>\n\u6442\u52d5\u7406\u8ad6\u306b\u57fa\u3065\u304f\u30b8\u30e7\u30eb\u30c0\u30f3\u7d30\u80de\u306e\u63a8\u5b9a<\/span>
\n\u25cb\u7fbd\u52e2\u6643\u5927\uff08\u6771\u4eac\u5927\u5b66\u7406\u5b66\u90e8\uff09\u3001\u9808\u7530\u793c\u4ec1\uff08\u6771\u4eac\u5927\u5b66\u60c5\u5831\u7406\u5de5\u5b66\u7cfb\u7814\u7a76\u79d1\uff09<\/span><\/p>\n\n\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u306e\u6570\u5024\u89e3\u6cd5\u306b\u304a\u3044\u3066\u3001\u5bfe\u89d2\u5316\u3067\u304d\u306a\u3044\u884c\u5217\u306e\u56fa\u6709\u5024\u3092\u6b63\u78ba\u306b\u6c42\u3081\u308b\u306e\u306f\u96e3\u3057\u3044\u3068\u3055\u308c\u3066\u3044\u308b\u3002\u3053\u308c\u306f\u3001\u5bfe\u89d2\u5316\u3067\u304d\u306a\u3044\u884c\u5217\u304c\u6301\u30642\u6b21\u4ee5\u4e0a\u306e\u30b8\u30e7\u30eb\u30c0\u30f3\u7d30\u80de\u304c\u8aa4\u5dee\u306e\u5f71\u97ff\u3092\u53d7\u3051\u3084\u3059\u3044\u3053\u3068\u304c\u539f\u56e0\u306e\u4e00\u3064\u3067\u3042\u308b\u3002\u5b9f\u969b\u3001k\u6b21\u306e\u30b8\u30e7\u30eb\u30c0\u30f3\u7d30\u80de\u3092\u6301\u3064\u884c\u5217\u306b\u8aa4\u5dee\u304c\u52a0\u308f\u308b\u3068\u56fa\u6709\u5024\u306fk\u500b\u306e\u7570\u306a\u308b\u56fa\u6709\u5024\u306b\u5206\u304b\u308c\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3092\u7528\u3044\u3066\u30b8\u30e7\u30eb\u30c0\u30f3\u6a19\u6e96\u5f62\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u3066\u304d\u305f\u3002\u672c\u8ad6\u6587\u3067\u306f\u307e\u305a\u3001\u30b8\u30e7\u30eb\u30c0\u30f3\u6a19\u6e96\u5f62\u3092\u6301\u3064\u884c\u5217\u306e\u6442\u52d5\u7406\u8ad6(Lidskii\u30fb1965)\u3092\u57fa\u306b\u3001\u884c\u5217\u306b\u8aa4\u5dee\u3092\u52a0\u3048\u3066\u7591\u4f3c\u30b9\u30da\u30af\u30c8\u30eb\u3092\u6c42\u3081\u3001\u305d\u306e\u7d50\u679c\u304c\u7406\u8ad6\u3068\u4e00\u81f4\u3059\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u3002\u3055\u3089\u306b\u3053\u306e\u7d50\u679c\u3092\u7528\u3044\u3066\u7591\u4f3c\u30b9\u30da\u30af\u30c8\u30eb\u3092\u898b\u308b\u3053\u3068\u3067\u5143\u306e\u884c\u5217\u306e\u8fd1\u508d\u306b\u5b58\u5728\u3059\u308b\u30b8\u30e7\u30eb\u30c0\u30f3\u7d30\u80de\u306e\u69cb\u9020\u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u306b\u90e8\u5206\u7684\u306b\u6210\u529f\u3057\u305f\u3002\n<\/div>\n
\u6570\u5024\u30b8\u30e7\u30eb\u30c0\u30f3\u5206\u89e3\u306b\u57fa\u3065\u304f\u884c\u5217\u4f59\u5f26\u95a2\u6570\u306e\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97<\/span>
\n\u25cb\u4f50\u85e4\u5927\uff08\u5ca9\u624b\u5927\u5b66\uff09\uff0c\u5bae\u5cf6\u4fe1\u4e5f\uff08\u5ca9\u624b\u5927\u5b66\uff09<\/span><\/p>\n\n\u8b1b\u6f14\u8005\u3089\u306f2019\u5e74\u65e5\u672c\u5fdc\u7528\u6570\u7406\u5b66\u4f1a\u7814\u7a76\u90e8\u4f1a\u9023\u5408\u767a\u8868\u4f1a\u306b\u304a\u3044\u3066, \u884c\u5217\u4f59\u5f26\u95a2\u6570\u306b\u5bfe\u3059\u308b\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u6cd5\u3092\u63d0\u6848\u3057\u3066\u3044\u308b. \u3053\u306e\u624b\u6cd5\u306f\u884c\u5217\u306e\u6570\u5024\u30b9\u30da\u30af\u30c8\u30eb\u5206\u89e3\u306b\u57fa\u3065\u304f\u3082\u306e\u3067\u3042\u308a, \u8fd1\u4f3c\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u304b\u3089\u6210\u308b\u884c\u5217\u304c\u60aa\u6761\u4ef6\u306e\u5834\u5408\u306b\u7834\u7dbb\u3059\u308b. \u672c\u8b1b\u6f14\u3067\u306f, \u8fd1\u4f3c\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u304b\u3089\u6210\u308b\u884c\u5217\u304c\u60aa\u6761\u4ef6\u3067\u3042\u3063\u3066\u3082\u7834\u7dbb\u3057\u306a\u3044\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u6cd5\u3092\u63d0\u6848\u3059\u308b. \u63d0\u6848\u3059\u308b\u624b\u6cd5\u306f\u6570\u5024\u30b8\u30e7\u30eb\u30c0\u30f3\u5206\u89e3\u306b\u57fa\u3065\u304f\u3082\u306e\u3067\u3042\u308b. \u6570\u5024\u4f8b\u306b\u3088\u308a, \u63d0\u6848\u3059\u308b\u624b\u6cd5\u306e\u7279\u5fb4\u3092\u793a\u3059.\n<\/div>\n
\u884c\u5217\u95a2\u6570\u306e\u30c8\u30ec\u30fc\u30b9\u306b\u5bfe\u3059\u308b\u9ad8\u901f\u306a\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u6cd5<\/span>
\n\u25cb\u9ed2\u7530\u65e9\u7d00\uff08\u5ca9\u624b\u5927\u5b66\uff09\uff0c\u5bae\u5cf6\u4fe1\u4e5f\uff08\u5ca9\u624b\u5927\u5b66\uff09<\/span><\/p>\n\n\u884c\u5217\u95a2\u6570\u306e\u30c8\u30ec\u30fc\u30b9\u306b\u5bfe\u3059\u308b\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u6cd5\u3092\u63d0\u6848\u3059\u308b. \u884c\u5217\u306e\u30c8\u30ec\u30fc\u30b9\u304c\u56fa\u6709\u5024\u306e\u7dcf\u548c\u3068\u4e00\u81f4\u3059\u308b\u3053\u3068\u306f\u3088\u304f\u77e5\u3089\u308c\u3066\u3044\u308b. \u63d0\u6848\u3059\u308b\u624b\u6cd5\u306f\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u305f\u3082\u306e\u3067\u3042\u308a, \u884c\u5217\u95a2\u6570\u305d\u306e\u3082\u306e\u3092\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u3067\u6c42\u3081\u308b\u306e\u3067\u306f\u306a\u304f,\u884c\u5217\u95a2\u6570\u306e\u56fa\u6709\u5024\u3092\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u3067\u6c42\u3081\u308b\u3053\u3068\u306b\u3088\u308a, \u884c\u5217\u95a2\u6570\u306e\u30c8\u30ec\u30fc\u30b9\u3092\u5305\u542b\u3059\u308b\u533a\u9593\u3092\u4e0e\u3048\u308b. \u6570\u5024\u5b9f\u9a13\u306b\u3088\u308a, \u63d0\u6848\u3059\u308b\u624b\u6cd5\u306e\u6709\u52b9\u6027\u3092\u793a\u3059.\n<\/div>\n
\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u69cb\u9020\u3092\u3082\u3064\u5927\u898f\u6a21\u884c\u5217\u306e\u5b9f\u6570\u4e57\u3068\u30d9\u30af\u30c8\u30eb\u306e\u7a4d\u306b\u5bfe\u3059\u308b\u9ad8\u901f\u306a\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u6cd5<\/span>
\n\u25cb\u5bae\u5cf6\u4fe1\u4e5f\uff08\u5ca9\u624b\u5927\u5b66\uff09<\/span><\/p>\n\nA, B \u3092\u305d\u308c\u305e\u308c m, n \u6b21\u6b63\u65b9\u884c\u5217, I_n \u3092 n \u6b21\u5358\u4f4d\u884c\u5217, \u2297\u3092\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u7a4d, c \u3092 mn \u6b21\u5143\u30d9\u30af\u30c8\u30eb, \u03b1 \u3092\u5b9f\u6570\u3068\u3059\u308b. \u672c\u8b1b\u6f14\u3067\u306f, (I_n \u2297 A + B \u2297 I_m)^\u03b1 c \u306b\u5bfe\u3059\u308b\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u6cd5\u3092\u63d0\u6848\u3059\u308b. \u3053\u306e\u5024\u306e\u8a08\u7b97\u306f\u975e\u6574\u6570\u968e\u30dd\u30a2\u30bd\u30f3\u65b9\u7a0b\u5f0f\u3092\u96e2\u6563\u5316\u3057\u305f\u969b\u7b49\u306b\u73fe\u308c\u308b. \u65e2\u5b58\u306e\u624b\u6cd5\u3092\u5229\u7528\u3057\u3066\u7cbe\u5ea6\u4fdd\u8a3c\u4ed8\u304d\u6570\u5024\u8a08\u7b97\u3092\u884c\u3046\u3068, m^3 n^3 \u3042\u308b\u3044\u306f m^4 n^4 \u306b\u6bd4\u4f8b\u3059\u308b\u6f14\u7b97\u56de\u6570\u304c\u5fc5\u8981\u3068\u306a\u308b. \u3053\u308c\u306b\u5bfe\u3057, \u63d0\u6848\u3059\u308b\u624b\u6cd5\u306f m^3 + n^3 \u306b\u6bd4\u4f8b\u3059\u308b\u6f14\u7b97\u56de\u6570\u3067\u5b9f\u884c\u53ef\u80fd\u3067\u3042\u308b. \u6570\u5024\u5b9f\u9a13\u7d50\u679c\u3092\u901a\u3058\u3066, \u63d0\u6848\u3059\u308b\u624b\u6cd5\u306e\u6709\u52b9\u6027\u3068\u9650\u754c\u3092\u5831\u544a\u3059\u308b.\n<\/div>\n
\u884c\u5217\u30fb\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5\u3068\u305d\u306e\u5fdc\u7528(3)\u3000\uff0813:30 – 14:50\uff09\u3000\u5ea7\u9577\uff1a\u5ca9\u4e0b \u6b66\u53f2\uff08\u5317\u6d77\u9053\u5927\u5b66\uff09<\/strong><\/p>\n\u884c\u5217\u4e00\u822c\u56fa\u6709\u5024\u554f\u984c\u306e\u4e00\u90e8\u306e\u56fa\u6709\u5bfe\u306e\u30d5\u30a3\u30eb\u30bf\u306e\u5229\u7528\u306b\u3088\u308b\u8fd1\u4f3c\u89e3\u6cd5\u306b\u3064\u3044\u3066<\/span>
\n\u25cb\u6751\u4e0a\u5f18\uff08\u6771\u4eac\u90fd\u7acb\u5927\u5b66\uff09<\/span><\/p>\n\n\u30d5\u30a3\u30eb\u30bf\u3092\u7528\u3044\u3066\u5b9f\u5bfe\u79f0\u5b9a\u5024\u4e00\u822c\u56fa\u6709\u5024\u554f\u984c\u306e\u56fa\u6709\u5bfe\u3067\u56fa\u6709\u5024\u304c\u4e0b\u7aef\u4ed8\u8fd1\u306e\u3082\u306e\u3092\u8fd1\u4f3c\u3057\u89e3\u304f\uff0e\u305d\u308c\u306b\u7528\u3044\u308b\u30d5\u30a3\u30eb\u30bf\u306f\uff0c\u56fa\u6709\u5024\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u305f\u30ec\u30be\u30eb\u30d9\u30f3\u30c8\u306e\u30b7\u30d5\u30c8\u304c\u7570\u306a\u308b\u3082\u306e\u306e\u7dda\u5f62\u7d50\u5408\u3092\u8003\u3048\u305d\u306e\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u591a\u9805\u5f0f\u3068\u3059\u308b\uff0e\u305d\u306e\u3088\u3046\u306a\u30d5\u30a3\u30eb\u30bf\u306e\u4f1d\u9054\u95a2\u6570\u306f\uff0c\u91cd\u8907\u3059\u308b\u6975\u3092\u6301\u305f\u306a\u3044\u7121\u9650\u9060\u3067\u6709\u754c\u306a\u6709\u7406\u95a2\u6570\u3068\u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u591a\u9805\u5f0f\u306e\u5408\u6210\u306b\u306a\u308b\uff0e\u8981\u6c42\u3059\u308b\u6761\u4ef6\u3092\u6e80\u305f\u3059\u6709\u7406\u95a2\u6570\u3092\u3046\u307e\u304f\u6c7a\u3081\u3066\u6027\u8cea\u306e\u826f\u3044\u30d5\u30a3\u30eb\u30bf\u3092\u69cb\u6210\u3059\u308b\u3053\u3068\u3092\u3081\u3056\u3059\uff0e\n<\/div>\n
\u975e\u5bfe\u79f0\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306b\u5bfe\u3059\u308b\u30ed\u30d0\u30b9\u30c8\u306a\u53f3\u524d\u51e6\u7406\u4ed8\u304dGPBiCGstab(L)\u6cd5<\/span>
\n\u25cb\u5800\u5185 \u4e00\u6a39\uff08\u6771\u4eac\u7406\u79d1\u5927\u5b66\uff09\uff0c\u76f8\u539f \u7814\u8f14\uff08\u6771\u4eac\u90fd\u5e02\u5927\u5b66\uff09\uff0c\u9234\u6728 \u4fca\u592b\uff08\u6771\u4eac\u7406\u79d1\u5927\u5b66\uff09\uff0c\u77f3\u6e21 \u6075\u7f8e\u5b50\uff08\u6771\u4eac\u7406\u79d1\u5927\u5b66\uff09<\/span><\/p>\n\nGPBiCGstab(L)\u6cd5\u306f\uff0c\u975e\u5bfe\u79f0\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306b\u6709\u52b9\u306a\u7a4d\u578b\u89e3\u6cd5\u306e\u4e00\u7a2e\u3067\u3042\u308b\uff0e\u3057\u304b\u3057\uff0c\u53f3\u524d\u51e6\u7406\u3092\u9069\u7528\u3059\u308b\u5834\u5408\uff0c\u52b9\u7387\u6027\u306e\u89b3\u70b9\u304b\u3089\u524d\u51e6\u7406\u884c\u5217\u306b\u95a2\u3059\u308b\u884c\u5217\u30d9\u30af\u30c8\u30eb\u7a4d\u3092\u5225\u306e\u30d9\u30af\u30c8\u30eb\u306e\u7dda\u5f62\u7d50\u5408\u3067\u4ee3\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\uff0c\u305d\u308c\u304c\u539f\u56e0\u3067\u6570\u5024\u7684\u4e0d\u5b89\u5b9a\u6027\u304c\u751f\u3058\u308b\uff0e\u305d\u3053\u3067\u672c\u7814\u7a76\u3067\u306f\uff0c\u524d\u51e6\u7406\u3092\u9069\u7528\u3059\u308b\u969b\u306b\uff0c\u4e0a\u8a18\u306e\u4ee3\u7528\u304c\u4e0d\u8981\u3068\u306a\u308b\u6539\u826f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u6848\u3059\u308b\uff0e\u6570\u5024\u5b9f\u9a13\u3092\u901a\u3057\u3066\uff0c\u53f3\u524d\u51e6\u7406\u3057\u305f\u63d0\u6848\u624b\u6cd5\u304c\u5f93\u6765\u306e\u65b9\u6cd5\u306b\u6bd4\u3079\u3066\u30ed\u30d0\u30b9\u30c8\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\n<\/div>\n
Flying restart\u4ed8\u304dCG\u6cd5\u306b\u5bfe\u3059\u308b\u6df7\u5408\u7cbe\u5ea6\u6f14\u7b97\u306b\u3088\u308b\u8fd1\u4f3c\u89e3\u7cbe\u5ea6\u306e\u5411\u4e0a<\/span>
\n\u25cb\u76f8\u539f \u7814\u8f14\uff08\u6771\u4eac\u90fd\u5e02\u5927\u5b66\uff09\uff0c\u5c3e\u5d0e \u514b\u4e45\uff08\u829d\u6d66\u5de5\u696d\u5927\u5b66\uff09\uff0c\u690b\u6728 \u5927\u5730\uff08\u7406\u5316\u5b66\u7814\u7a76\u6240\uff09<\/span><\/p>\n\nFlying restart\u306f\uff0c\u53cd\u5fa9\u6cd5\u306eresidual gap\u3092\u6539\u5584\u3057\uff0c\u771f\u306e\u6b8b\u5dee\u3092\u6e1b\u5c11\u3055\u305b\u308b\u624b\u6cd5\u3067\u3042\u308b\uff0e\u3057\u304b\u3057\uff0c\u30ea\u30b9\u30bf\u30fc\u30c8\u5468\u671f\u306a\u3069\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u8abf\u6574\u304c\u96e3\u3057\u304f\uff0c\u307e\u305f\u8aa4\u5dee\u306e\u89b3\u70b9\u3067\u306f\u7cbe\u5ea6\u304c\u5411\u4e0a\u3057\u306a\u3044\u5834\u5408\u304c\u3042\u308b\uff0e\u672c\u8b1b\u6f14\u3067\u306f\uff0c\u30ea\u30b9\u30bf\u30fc\u30c8\u306b\u4ed8\u968f\u3059\u308b\u90e8\u5206\u306e\u307f\u9ad8\u7cbe\u5ea6\u306b\u8a08\u7b97\u3059\u308b\u6df7\u5408\u7cbe\u5ea6\u6f14\u7b97\u306b\u3088\u308a\uff0c\u7d30\u304b\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u8abf\u6574\u3092\u3059\u308b\u3053\u3068\u306a\u304f\u7c21\u4fbf\u306b\u8aa4\u5dee\u3092\u6e1b\u5c11\u3055\u305b\u308b\u624b\u6cd5\u3092\u63d0\u6848\u3059\u308b\uff0eCG\u6cd5\u306b\u5bfe\u3059\u308b\u6570\u5024\u5b9f\u9a13\u3092\u901a\u3057\u3066\uff0c\u7279\u306b\u8aa4\u5dee\u304c\u505c\u6ede\u3059\u308b\u60aa\u6761\u4ef6\u554f\u984c\u306b\u5bfe\u3057\uff0c\u63d0\u6848\u624b\u6cd5\u304c\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\n<\/div>\n
GMRES Methods for Tomographic Reconstruction with an Unmatched Back Projector<\/span>
\nPer Christian HANSEN (Technical University of Denmark), \u25cbKen HAYAMI (Professor Emeritus, National Institute of Informatics), Keiichi MORIKUNI (University of Tsukuba)<\/span><\/p>\n\nUnmatched pairs of forward and back projectors are common in X-ray CT computations due to the need for fast algorithms that best utilize the computer hardware. We propose using preconditioned GMRES (AB-,BA-GMRES) to handle the unmatched normal equations. They are simple to implement and rely only on available forward and back projectors. They are equivalent to LSQR and LSMR in the case of a matched projector pair. Numerical experiments show that they exhibit a desired semi-convergence behavior and are suited for large-scale CT reconstruction problems with noisy data.\n<\/div>\n
\u884c\u5217\u30fb\u56fa\u6709\u5024\u554f\u984c\u306e\u89e3\u6cd5\u3068\u305d\u306e\u5fdc\u7528(4)\u3000\uff0815:00 – 15:40\uff09\u3000\u5ea7\u9577\uff1a\u5bae\u5cf6 \u4fe1\u4e5f\uff08\u5ca9\u624b\u5927\u5b66\uff09<\/strong><\/p>\nA unified extension of convergence analyses to optimization with Cayley transform over Stiefel manifold<\/span>
\n\u25cb\u4e45\u7c73\u5553\u592a\uff08\u6771\u4eac\u5de5\u696d\u5927\u5b66\uff09, \u5c71\u7530\u529f\uff08\u6771\u4eac\u5de5\u696d\u5927\u5b66\uff09<\/span><\/p>\n\nBy using generalized Cayley transforms, an optimization problem over the Stiefel manifold can be translated into another optimization problem over a vector space possibly changing after a certain period. Such an adaptive translation enables us to apply directly many powerful optimization techniques, designed originally over a vector space, to a translated problem within each period. We present a unified convergence analysis of optimization algorithms along this translation strategy.\n<\/div>\n
\u8907\u6570\u6a5f\u95a2\u304c\u5206\u6563\u4fdd\u6301\u3059\u308b\u79d8\u533f\u30c7\u30fc\u30bf\u306b\u5bfe\u3059\u308b\u30c7\u30fc\u30bf\u30b3\u30e9\u30dc\u30ec\u30fc\u30b7\u30e7\u30f3\u89e3\u6790\u6280\u8853<\/span>
\n\u25cb\u4eca\u5009\u6681\uff08\u7b51\u6ce2\u5927\u5b66\uff09\u3001\u5ca1\u7530\u5e78\u5f66\uff08\u7b51\u6ce2\u5927\u5b66\uff09\u3001\u6afb\u4e95\u9244\u4e5f\uff08\u7b51\u6ce2\u5927\u5b66\uff09<\/span><\/p>\n\n\u533b\u7642\u30fb\u5275\u85ac\u30fb\u91d1\u878d\u30fb\u3082\u306e\u3065\u304f\u308a\u306a\u3069\u591a\u69d8\u306a\u5206\u91ce\u306b\u304a\u3044\u3066\uff0c\u30c7\u30fc\u30bf\u89e3\u6790\u306e\u305f\u3081\u306b\uff0c\u751f\u30c7\u30fc\u30bf\u3092\u5171\u6709\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3042\u308b\u5834\u5408\u304c\u3042\u308b\uff0e\u3053\u306e\u3088\u3046\u306a\u5206\u6563\u30c7\u30fc\u30bf\u975e\u5171\u6709\u7d71\u5408\u89e3\u6790\u6280\u8853\u3068\u3057\u3066Google\u304c\u958b\u767a\u3057\u305fFederated Learning\u304c\u6ce8\u76ee\u3092\u96c6\u3081\u3066\u3044\u308b\uff0e\u8fd1\u5e74\uff0c\u6211\u3005\u306fFederated Learning\u3068\u306f\u7570\u306a\u308b\u6226\u7565\u3067\u5206\u6563\u30c7\u30fc\u30bf\u975e\u5171\u6709\u7d71\u5408\u89e3\u6790\u3092\u53ef\u80fd\u3068\u3059\u308b\u30c7\u30fc\u30bf\u30b3\u30e9\u30dc\u30ec\u30fc\u30b7\u30e7\u30f3\u89e3\u6790\u6280\u8853\u306e\u958b\u767a\u3092\u9032\u3081\u3066\u3044\u308b\uff0e\u672c\u8b1b\u6f14\u3067\u306f\uff0c\u30c7\u30fc\u30bf\u30b3\u30e9\u30dc\u30ec\u30fc\u30b7\u30e7\u30f3\u89e3\u6790\u306e\u6982\u8981\u3092\u793a\u3057\uff0c\u6570\u5024\u5b9f\u9a13\u304b\u3089\u305d\u306e\u6709\u52b9\u6027\u3092\u793a\u3059\uff0e\n<\/div>\n\n\n
\u8b1b\u6f14\u7533\u3057\u8fbc\u307f<\/h2><\/h2>\n\u8b1b\u6f14\u52df\u96c6\u306f\u7de0\u3081\u5207\u308a\u307e\u3057\u305f\u3002\n\n\n\n
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