{"id":1121,"date":"2008-05-14T22:22:30","date_gmt":"2008-05-14T13:22:30","guid":{"rendered":"http:\/\/na-inet.jp\/new-na-inet\/weblog\/2008\/05\/njhigham_functions_of_matrices\/"},"modified":"2008-05-14T22:22:30","modified_gmt":"2008-05-14T13:22:30","slug":"njhigham_functions_of_matrices","status":"publish","type":"post","link":"https:\/\/na-inet.jp\/weblog2\/2008\/05\/14\/njhigham_functions_of_matrices\/","title":{"rendered":"N.J.Higham, &#8220;Functions of Matrices &#8211; Theory and Computation&#8221;, SIAM"},"content":{"rendered":"<p>[ <a href=\"http:\/\/www.amazon.co.jp\/gp\/product\/0898716462?ie=UTF8&#038;tag=pasnet-22&#038;linkCode=as2&#038;camp=247&#038;creative=1211&#038;creativeASIN=0898716462\">Amazon<\/a>, <a href=\"http:\/\/www.siam.org\/books\/ot104\/\">SIAM<\/a> ] ISBN 978-0-89871-646-7, $59<br \/>\n<a href=\"http:\/\/na-inet.jp\/weblog\/archives\/functions_of_matrices.png\"><img loading=\"lazy\" decoding=\"async\" alt=\"functions_of_matrices.png\" src=\"http:\/\/na-inet.jp\/weblog\/archives\/functions_of_matrices-thumb.png\" width=\"100\" height=\"141\" \/><\/a><br \/>\n\u3000\u56db\u5341\u5e74\u8fd1\u304f\u8aad\u66f8\u4eba\u3092\u6c17\u53d6\u3063\u3066\u3044\u308b\u3068\uff0c\u81ea\u5206\u306a\u308a\u306b\u69cb\u7bc9\u3057\u305f\u300c\u8457\u8005\u540d\u5373\u8cb7\u3044\u30ea\u30b9\u30c8\u300d\u306a\u308b\u3082\u306e\u304c\u30ac\u30c3\u30c1\u30ea\u7d44\u307f\u4e0a\u304c\u3063\u3066\u3044\u308b\u3002\u30ef\u30b7\u306e\u982d\u8133\u306e\u30ad\u30e3\u30c3\u30b7\u30e5\u30e1\u30e2\u30ea\u306b\u306f\u5e38\u306b\u3053\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u84c4\u7a4d\u3055\u308c\u3066\u304a\u308a\uff0c\u3053\u308c\u306b\u5f15\u3063\u304b\u304b\u3063\u305f\u8457\u8005\u306e\u65b0\u520a\u304c\u51fa\u308b\u306e\u3092\u77e5\u308b\u3068\u30d1\u30d6\u30ed\u30d5\u306e\u72ac\u3088\u308a\u65e9\u304f\u53cd\u5c04\u795e\u7d4c\u3067\u8cb7\u3063\u3066\u3057\u307e\u3046\u306e\u3067\u3042\u308b\u3002\u3067\uff0c\u672c\u66f8\u3082\u3054\u591a\u5206\u306b\u6f0f\u308c\u305a\uff0cSIAM News\u306b\u544a\u77e5\u304c\u51fa\u305f\u306e\u3092\u898b\u308b\u304c\u65e9\u3044\u304b\uff0c\u65e9\u901fSIAM\u4f1a\u54e1\u4fa1\u683c\u3067\u6ce8\u6587\u3092\u304b\u3051\u3066\u5165\u624b\u3057\u305f\u8a33\u3067\u3042\u308b\u3002<br \/>\n\u3000Sylvester\u3068Cayley\u3063\u3066\u306e\u306f\uff0c\u4eca\u306e\u6570\u5024\u8a08\u7b97\u5c4b\u306a\u3089\u77e5\u3089\u306c\u30e2\u30ce\u306e\u306a\u3044\u53e4\u5178\u7684\u306a\u540d\u524d\u3060\u304c\uff0c\u3053\u306e\u4e8c\u4eba\u306f19\u4e16\u7d00\u5f8c\u534a\u306e\u30a4\u30ae\u30ea\u30b9\u7dda\u578b\u4ee3\u6570\u6d3e\u306e\u30e1\u30f3\u30d0\u30fc\u3068\u3057\u3066\uff0c\u751f\u6daf\u3092\u901a\u3058\u305f\u30b3\u30f3\u30d3\u3067\u6d3b\u8e8d\u3057\u305f\u6570\u5b66\u8005\u3067\u3042\u308b(\u68ee\u6bc5\u300c<a href=\"http:\/\/www.amazon.co.jp\/gp\/product\/4480086587?ie=UTF8&#038;tag=pasnet-22&#038;linkCode=as2&#038;camp=247&#038;creative=1211&#038;creativeASIN=4480086587\">\u7570\u8aac\u6570\u5b66\u8005\u5217\u4f1d<\/a>\u300d\u3061\u304f\u307e\u5b66\u82b8\u6587\u5eab, P.154-160)\u3002\u7dda\u578b\u4ee3\u6570\u3092\u304b\u3058\u3063\u305f\u4eba\u9593\u306a\u3089\uff0c\u884c\u5217A\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u6642\u306b\u306f\u81ea\u7136\u3068|xI-A|=0\u3092\u89e3\u304f\u3067\u3042\u308d\u3046\u304c\uff0c\u3053\u308c\u304cHamilton-Cayley\u306e\u5b9a\u7406\u3063\u3066\u5974\u3067\u3042\u308b(\u658e\u85e4\u6b63\u5f66\u300c<a href=\"http:\/\/www.amazon.co.jp\/gp\/product\/4130620010?ie=UTF8&#038;tag=pasnet-22&#038;linkCode=as2&#038;camp=247&#038;creative=1211&#038;creativeASIN=4130620010\">\u7dda\u578b\u4ee3\u6570\u5b66<\/a>\u300d\u6771\u5927\u51fa\u7248\u4f1a, P.198)\u3002\u68ee\u306b\u3088\u308c\u3070\u3053\u306e\u4e8c\u4eba\u304c\u51fa\u4f1a\u3063\u305f\u306e\u306f\u6570\u5b66\u7814\u7a76\u4f1a\u3068\u304b\u3067\u306f\u306a\u304f\uff0c\u6cd5\u5f8b\u5bb6\u306b\u306a\u308b\u305f\u3081\u306e\u5b66\u6821\u3060\u3063\u305f\u3068\u3044\u3046\u306e\u3060\u304b\u3089\uff0c\u4e16\u306e\u4e2d\u3069\u3093\u306a\u51fa\u4f1a\u3044\u304c\u3042\u308b\u304b\u308f\u304b\u3089\u3093\u30e2\u30f3\u3060\u3002<br \/>\n\u3000\u3067\uff0c\u672c\u66f8\u306e\u30bf\u30a4\u30c8\u30eb\u3067\u3042\u308b\u300c\u884c\u5217\u95a2\u6570\u300d\u3063\u3066\u306e\u306f\uff0c\u3053\u306eCayley\u3068Sylvester\u306b\u7aef\u3092\u767a\u3059\u308b\uff0c\u3068\u3044\u3046\u3088\u308a\uff0cCayley\u306fA^(1\/2)\uff0cSylverster\u306a\u3093\u3066\u305d\u306e\u3082\u306e\u30ba\u30d0\u30ea\u3092\u6700\u521d\u306b\u63d0\u5531\u3057\u305f\u3089\u3057\u3044\u306e\u3067\u3042\u308b\u3002\u3078\u3047\uff5e\u30fb\u30fb\u30fb\u3068\u3044\u3046\u6240\u304b\u3089\u672c\u66f8\u306f\u59cb\u307e\u3063\u3066\u3044\u308b\u3002<br \/>\n\u3000\u4e00\u4f53\u305d\u3093\u306a\u3082\u306e\u304c\u4f55\u306e\u5f79\u306b\u7acb\u3064\u306e\u304b\u30fb\u30fb\u30fb\u3068\u3044\u3076\u304b\u308b\u4eba\u306f\u3069\u306e\u3050\u3089\u3044\u3044\u308b\u306e\u304b\u3057\u3089\uff1f\u3000exp(A)\u306a\u3093\u3066\u306e\u306f\u7dda\u578b\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u8868\u73fe\u306b\u306f\u5fc5\u8981\u3060\u3057\uff0c\u305d\u308c\u3092\u5ef6\u9577\u3057\u3066\u3044\u3051\u3070sin(A)\u3068\u304blog(A)\u3068\u304b\u3082\u540c\u69d8\u306b\u8003\u3048\u3089\u308c\u3066\uff0c\u305d\u308c\u306a\u308a\u306b\u5fdc\u7528\u304c\u3042\u308a\u305d\u3046\u306a\u6c17\u306f\u3057\u3066\u304f\u308b\u3002\u3067\uff0c\u500b\u3005\u306b\u95a2\u6570\u3092\u5897\u3084\u3057\u3066\u3050\u3089\u3044\u306a\u3089\uff0c\u3044\u3063\u305d\u306e\u3053\u3068\u30b9\u30ab\u30e9\u30fc\u95a2\u6570f(t)\u3092\u305d\u306e\u307e\u307e\u62e1\u5f35\u3057\u3066\u884c\u5217\u95a2\u6570f(A)\u3092\u5b9a\u7fa9\u3067\u304d\u306a\u3044\u304b\uff0c\u3068\u8003\u3048\u308b\u306e\u306f\uff0c\u3054\u304f\u5e38\u8b58\u7684\u306a\u601d\u8003\u3067\u3042\u308b\u3002<a href=\"http:\/\/www.maths.manchester.ac.uk\/~higham\/\">\u30de\u30f3\u5927\u306e\u30df\u30b9\u30bf\u30fc\u30b9\u30dd\u30c3\u30af\u535a\u58eb<\/a>\u3053\u3068N.J.Higham\u306f\u3053\u306e\u65b9\u5411\u30673\u3064\u306ef(A)\u306e\u5b9a\u7fa9\u65b9\u6cd5\u3092\u5ef6\u3079\uff0cf(t)\u304c\u89e3\u6790\u7684\u3067\u3042\u308c\u3070\u3053\u308c\u3089\u304c\u4e92\u3044\u306b\u540c\u5024\u3067\u3042\u308b\u3053\u3068\u3092<a href=\"http:\/\/www.siam.org\/books\/ot104\/OT104HighamChapter1.pdf\">\u7b2c\u4e00\u7ae0<\/a>(PDF)\u3067\u30ad\u30c3\u30c1\u30ea\u8a3c\u660e\u3057\u3066\u3044\u308b\u3002\u3075\u30fc\u3093\uff0c\u307e\u3041Jordan\u6a19\u6e96\u5f62\u306e\u306f\u5206\u304b\u308b\u3068\u3057\u3066\uff0cHermite\u88dc\u9593\u3068Cauchy\u306e\u7a4d\u5206\u8868\u793a\u304c\u7e4b\u304c\u308b\u3068\u306f\u77e5\u3089\u306a\u304b\u3063\u305f\u306a\u3041\u3002\u3063\u3066\u7121\u77e5\u306b\u3082\u7a0b\u304c\u3042\u308b\u3063\u3066\u304b\uff1f<br \/>\n\u3000\u30ef\u30b7\u304c\u4e00\u756a\u8208\u5473\u304c\u3042\u308b\u306e\u304c\u5fdc\u7528\u5206\u91ce(\u7b2c2\u7ae0)\u3068\uff0cexp(A)\u306e\u8a71\u984c(\u7b2c10\u7ae0)\u306a\u3093\u3060\u304c\uff0c\u3053\u306e\u8fba\u308a\u3092\u542b\u3081\u3066\u672c\u66f8\u3092\u773a\u3081\u3066\u307f\u308b\u3068\uff08\u8aad\u3093\u3060\uff0c\u3067\u306f\u306a\u3044\u304b\u3089\u306d\u70ba\u5ff5)\uff0c\u7247\u3063\u7aef\u304b\u3089\u60c5\u5831\u3092\u96c6\u3081\u307e\u304f\u3063\u3066\u66f8\u304d\u307e\u304f\u3063\u305f<a href=\"http:\/\/www.maths.manchester.ac.uk\/~higham\/asna\/index.php\">\u4ee5\u524d\u306e\u8457\u4f5c<\/a>\u306b\u6bd4\u3079\u308b\u3068\uff0c\u666e\u901a\u306e\u6570\u5b66\u66f8\u306e\u3088\u3046\u306b\u8a71\u984c\u304c\u7a4d\u307f\u4e0a\u3052\u3089\u308c\u3066\u5c55\u958b\u3055\u308c\u3066\u3044\u308b\u5370\u8c61\u304c\u3042\u308b\u3002\u30b9\u30dd\u30c3\u30af\u535a\u58eb\u306b\u3088\u308c\u3070\uff0c\u6700\u521d\u306e\u7ae0\u4ee5\u5916\u306f\u72ec\u7acb\u3057\u3066\u8aad\u3081\u308b\u3068\u8a00\u3063\u3066\u3044\u308b\u304c\uff0c\u6700\u521d\u304b\u3089\u3058\u3063\u304f\u308a\u8aad\u3093\u3060\u65b9\u304c\u70ba\u306b\u306a\u308a\u305d\u3046\u306a\u611f\u3058\u304c\u3059\u308b\u3002\u8a71\u984c\u3068\u3057\u3066\u9078\u3093\u3067\u3044\u308b\u306e\u306fO(n^4)\u3092\u8d8a\u3048\u306a\u3044\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u843d\u3061\u7740\u304f\u3082\u306e\u306b\u7d5e\u3063\u3066\u3044\u308b\u305d\u3046\u3060\u304c\uff0c\u3053\u306e\u8fba\u308a\u306f\u6570\u5024\u8a08\u7b97\u5c4b\u3089\u3057\u3044\uff0c\u3068\u540c\u6642\u306b\uff0c\u5177\u4f53\u7684\u3067\u69cb\u7bc9\u7684\u306a\u30a4\u30ae\u30ea\u30b9\u6570\u5b66\u306e\u4f1d\u7d71(by \u85e4\u539f\u6b63\u5f66)\u306b\u3082\u5fe0\u5b9f\u3068\u3044\u3046\u3053\u3068\u306a\u3093\u3060\u308d\u3046\u306a\u3041\u3002<br \/>\n\u3000\u500b\u4eba\u7684\u306b\u306f\uff0c\u3082\u3046\u3061\u3063\u3068\u73fe\u72b6\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u74b0\u5883\u306b\u3064\u3044\u3066\u3082\u8a00\u53ca\u3057\u3066\u6b32\u3057\u304b\u3063\u305f\u306a\uff0c\u3068\u3044\u3046\u4e0d\u6e80\u304c\u3042\u308b\u3002\u4eca\u3067\u306f\u30b3\u30f3\u30b7\u30e5\u30fc\u30de\u5411\u3051CPU\u3067\u3082\u30de\u30eb\u30c1\u30b3\u30a2\u5316\u3084SIMD\u547d\u4ee4\u306e\u5145\u5b9f\u304c\u306a\u3055\u308c\u3066\u3044\u308b\u306e\u3067\uff0c\u30e1\u30a4\u30f3\u30e1\u30e2\u30ea\u306b\u5165\u308a\u5207\u308b\u7a0b\u5ea6\u306b\u5927\u898f\u6a21\u306a\u884c\u5217\u30fb\u30d9\u30af\u30c8\u30eb\u8a08\u7b97\u304c\u304b\u306a\u308a\u9ad8\u901f\u306b\u5b9f\u884c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u304d\u3066\u3044\u308b\u3002\u6570\u5024\u8a08\u7b97\u6027\u80fd\u3092\u6e2c\u308b\u6642\u306b\u306f\u884c\u5217\u7a4d\u8a08\u7b97\u3092\u884c\u3046\u306e\u304c\u666e\u901a\u3060\u304c\uff0c\u304d\u3061\u3093\u3068\u30c1\u30e5\u30fc\u30cb\u30f3\u30b0\u3055\u308c\u305f<a href=\"http:\/\/math-atlas.sourceforge.net\/\">ATLAS<\/a>(\u306eDGEMM\u95a2\u6570)\u3092\u4f7f\u3048\u3070\uff0c\u5c11\u3057\u578b\u843d\u3061\u3057\u305fCPU\u5358\u4f53\u3067\u3082\u6570GFLOPS\u306e\u6027\u80fd\u304c\u5b89\u5b9a\u3057\u3066\u53e9\u304d\u51fa\u305b\u308b(\u4f8b\u3048\u3070<a href=\"http:\/\/na-inet.jp\/research\/akita2006.pdf\">\u3053\u306ePDF\u306e16\u679a\u76ee\u306e\u30b9\u30e9\u30a4\u30c9<\/a>\u3092\u53c2\u7167)\u3002\u9006\u306b\u8a00\u3048\u3070\uff0c\u5171\u6709\u30e1\u30e2\u30ea\u5185\u4e26\u5217\u74b0\u5883\u3067\u5341\u5206\u306a\u898f\u6a21\u306e\u8a08\u7b97\u306a\u3089\uff0c\u3061\u3087\u3063\u3068\u3050\u3089\u3044\u8a08\u7b97\u91cf\u304c\u5897\u3048\u3066\u3082\u884c\u5217\u5358\u4f4d\u3067\u307e\u3068\u3081\u3066\u8a08\u7b97\u3057\u305f\u65b9\u304c\u52b9\u7387\u304c\u826f\u304f\u306a\u308b\u53ef\u80fd\u6027\u3082\u3042\u308b\u306e\u3060\u3002\u8fd1\u9803\u3067\u306f\u305d\u3053\u306b\u6c17\u304c\u4ed8\u3044\u305f\u65b9\u3005\u304c\u3044\u308d\u3044\u308d\u3084\u308a\u51fa\u3057\u3066\u3044\u308b\u3088\u3046\u3067\u3042\u308b\u3002<br \/>\n\u3000\u3053\u306e\u3088\u3046\u306b\uff0c\u4eca\u306ePC\u74b0\u5883\u306f\u884c\u5217\u8a08\u7b97\u306b\u5411\u3044\u3066\u3044\u308b\u306e\u3067\u3042\u308b\u304b\u3089\u3057\u3066\uff0c\u672c\u66f8\u3067\u63d0\u6848\u3057\u3066\u3044\u308b\u884c\u5217\u95a2\u6570\u306e\u8a08\u7b97\u306e\u5b9f\u9a13\u306b\u306f\u3082\u3063\u3066\u3053\u3044\u3067\u3042\u308b\u3002\u672c\u66f8\u306e\u8a08\u7b97\u306f<a href=\"http:\/\/www.mathworks.com\/\">Matlab<\/a>(\u306e\u500d\u7cbe\u5ea6\u8a08\u7b97)\u3067\u884c\u3063\u3066\u3044\u308b\u304c\uff0c\u3053\u308c\u3060\u3063\u3066\u3053\u306e\u3088\u3046\u306a\u74b0\u5883\u304c\u6574\u3063\u3066\u3044\u3066\u3053\u305d\u6c17\u8efd\u306b\u5b9f\u9a13\u3067\u304d\u308b\u306e\u3067\u3042\u308b\u3002<br \/>\n\u3000\u3064\u30fc\u3053\u3068\u3067\uff0cexp(A)\u3069\u307e\u308a\u306a\u3089\u3068\u3082\u304b\u304f\uff0cf(A)\u307e\u3067\u5e83\u3052\u3066\u4f55\u306e\u5f79\u306b\u7acb\u3064\u3093\u3060\u3068\u304b\u30d6\u30fc\u305f\u308c\u308b\u3088\u308a\uff0c\u6298\u89d2\u306e\u884c\u5217\u8a08\u7b97\u5411\u304dPC\u74b0\u5883\u3092\u4f7f\u3044\u5012\u3057\u3066\u904a\u3093\u3060\u65b9\u304c\uff0c\u4eba\u751f\u697d\u3057\u304f\u306a\u308b\u3093\u3058\u3083\u306a\u3044\u304b\u3068\uff0c\u81ea\u5206\u52dd\u624b\u306b\u601d\u3046\u4eca\u65e5\u3053\u306e\u9803\u3067\u3042\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ Amazon, SIAM ] ISBN 978-0-89871-646-7, $59 \u3000\u56db\u5341\u5e74\u8fd1\u304f\u8aad\u66f8\u4eba\u3092\u6c17\u53d6\u3063\u3066\u3044\u308b\u3068\uff0c\u81ea\u5206\u306a\u308a\u306b\u69cb\u7bc9\u3057\u305f\u300c\u8457\u8005\u540d\u5373\u8cb7\u3044\u30ea\u30b9\u30c8\u300d\u306a\u308b\u3082\u306e\u304c\u30ac\u30c3\u30c1\u30ea\u7d44\u307f\u4e0a\u304c\u3063\u3066\u3044\u308b\u3002\u30ef\u30b7\u306e\u982d\u8133\u306e\u30ad\u30e3\u30c3 &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/na-inet.jp\/weblog2\/2008\/05\/14\/njhigham_functions_of_matrices\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;N.J.Higham, &#8220;Functions of Matrices &#8211; Theory and Computation&#8221;, SIAM&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","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":[3],"tags":[],"class_list":["post-1121","post","type-post","status-publish","format-standard","hentry","category-3"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/posts\/1121","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=1121"}],"version-history":[{"count":0,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/posts\/1121\/revisions"}],"wp:attachment":[{"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/media?parent=1121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/categories?post=1121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/na-inet.jp\/weblog2\/wp-json\/wp\/v2\/tags?post=1121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}