{"id":586,"date":"2015-09-29T11:12:07","date_gmt":"2015-09-29T02:12:07","guid":{"rendered":"http:\/\/cs-tklab.na-inet.jp\/?p=586"},"modified":"2015-10-06T08:20:12","modified_gmt":"2015-10-05T23:20:12","slug":"%e6%a8%a1%e6%93%ac%e8%ac%9b%e7%be%a92-%e5%a4%a7%e8%a6%8f%e6%a8%a1%e8%a8%88%e7%ae%97%e3%81%a8cpu%ef%bc%86gpu","status":"publish","type":"post","link":"https:\/\/kd-tklab.na-inet.jp\/?p=586","title":{"rendered":"[\u6a21\u64ec\u8b1b\u7fa92] \u5927\u898f\u6a21\u8a08\u7b97\u3068CPU\uff06GPU"},"content":{"rendered":"


\n\u3000\u3053\u308c\u306f\u6a21\u64ec\u8b1b\u7fa9\u300c\u6570\u5b66\u3068\u8a08\u7b97\u3000\uff5e\u7406\u8ad6\u3068\u5b9f\u8df5\uff5e<\/a>\u300d\u306e\u7d9a\u304d\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305a\u305d\u3061\u3089<\/a>\u3092\u8aad\u3093\u3067\u9802\u3044\u3066\u304b\u3089\uff0c\u3053\u3061\u3089\u306e\u6587\u7ae0\u306b\u53d6\u308a\u7d44\u3093\u3067\u4e0b\u3055\u3044\u3002<\/p>\n

1. \u5927\u898f\u6a21\u8a08\u7b97\u3068\u306f\uff1f<\/strong><\/p>\n

\u3000\u5927\u898f\u6a21\u8a08\u7b97\u3068\u306f\uff0c\u73fe\u5728\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u304c\u5b9f\u884c\u3059\u308b\u306b\u969b\u3057\uff0c\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u30e1\u30e2\u30ea\u306b\u683c\u7d0d\u3057\uff0c\u8a08\u7b97\u6642\u9593\u306b\u3082\u6570\u79d2\uff0c\u6570\u5206\uff0c\u6570\u6642\u9593\u30fb\u30fb\u30fb\u6570\u65e5\u30fb\u30fb\u30fb\u8cbb\u3084\u3059\u5fc5\u8981\u306e\u3042\u308b\u4e00\u9023\u306e\u8a08\u7b97\u51e6\u7406\u306e\u3053\u3068\u3067\u3059\u3002
\n\u3000\u65e2\u306b\u304a\u8a71\u3057\u3057\u305f\u901a\u308a\uff0c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\uff0c\u51e6\u7406\u3059\u308b\u5bfe\u8c61\u3068\u306a\u308b\u30c7\u30fc\u30bf\u3092\u4e00\u5ea6\u30e1\u30e2\u30ea\u306b\u683c\u7d0d\u3057\uff0cCPU\u3067\u305d\u308c\u3089\u3092\u8aad\u307f\u8fbc\u3093\u3067\u51e6\u7406\u3057\uff0c\u51e6\u7406\u7d50\u679c\u3092\u30e1\u30e2\u30ea\u306b\u66f8\u304d\u623b\u3059\u3068\u3044\u3046\u4f5c\u696d\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002\u3053\u306e\u4f5c\u696d1\u56de\u5206\u306e\u51e6\u7406\u6642\u9593\u306f\u3054\u304f\u77ed\u304f\uff0c\u30de\u30a4\u30af\u30ed\u79d2(\u03bcs)\\(=10^{-6}\\)\u79d2\u5358\u4f4d\u306e\u4e16\u754c\u3067\u3059\u3002\u3057\u304b\u3057\u4f8b\u3048\u30705\u03bcs\u306e\u51e6\u7406\u309210\u56de\u884c\u3048\u307050\u03bcs\uff0c100\u56de\u884c\u3048\u3070500\u03bcs\uff0c…\u3068\uff0c\u7e70\u308a\u8fd4\u3057\u306e\u6570\\(n\\)\u304c\u5927\u304d\u304f\u306a\u308c\u3070\u306a\u308b\u307b\u3069\uff0c\u5408\u8a08\u51e6\u7406\u6642\u9593\\(5n\\) \u03bcs\u306f\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\\(n\\)\u306b\u6bd4\u4f8b\u3057\u3066\u6642\u9593\u304c\u5897\u3048\u308b\u51e6\u7406\u306e\u3053\u3068\u3092\u300c\\(O(n)\\)\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3068\u79f0\u3057\u307e\u3059\u3002\u5148\u306b\u6319\u3052\u305f\u5e73\u5747\u306e\u8a08\u7b97
\n\\[ \\mu = \\frac{1}{n} \\sum^n_{i=1} c_i = \\frac{c_1 + c_2 + \\cdots + c_n}{n} \\]
\n\u306f\u5178\u578b\u7684\u306a\\(O(n)\\)\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002<\/p>\n

\u3000\u3057\u304b\u3057\uff0c\u5b9f\u7528\u7684\u306a\u51e6\u7406\u306e\u5834\u5408\uff0c\u898f\u6a21\uff0c\u5373\u3061\\(n\\)\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u3082\u3063\u3068\u5927\u304d\u306a\u51e6\u7406\u6642\u9593\u3092\u8981\u3059\u308b\u3082\u306e\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u5c11\u3057\u8a71\u304c\u96e3\u3057\u304f\u306a\u308a\u307e\u3059\u304c\uff0c\u4ee5\u4e0b\u3067\u306f\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\uff08\u9023\u7acb\u65b9\u7a0b\u5f0f\u306e\u4e00\u7a2e\uff09\u3092\u898b\u3066\u3044\u304f\u3053\u3068\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n

2. \u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3068\u5927\u898f\u6a21\u5316<\/strong><\/p>\n

\u3000\u5b9f\u6570\u306e\u5b9a\u6570\\(a\\), \\(b\\), \\(c\\), \\(d\\)\u306b\u5bfe\u3057\u3066\uff0c\u6b21\u306e\u4e8c\u3064\u306e\u65b9\u7a0b\u5f0f\u3092\u540c\u6642\u306b\u6e80\u8db3\u3059\u308b\u89e3\\(x\\), \\(y\\)\u3092\u6c42\u3081\u308b\uff0c\u3068\u3044\u3046\u306e\u304c\uff0c\u4e2d\u5b66\u6821\u3067\u521d\u3081\u3066\u7fd2\u3046\u9023\u7acb\u65b9\u7a0b\u5f0f\uff0c\u6b63\u5f0f\u306b\u306f\u9023\u7acb\u300c\u4e00\u6b21\u300d\u65b9\u7a0b\u5f0f\u3067\u3059\u3002<\/p>\n

\\[\\left\\{\\begin{array}{ccc} ax + by &=& \\alpha \\\\
\n cx + dy &=& \\beta \\end{array}\\right. \\]<\/p>\n

\u3000\u5177\u4f53\u7684\u306b\u306f\u4f8b\u3048\u3070<\/p>\n

\\[\\left\\{\\begin{array}{ccc} 3x + 2y &=& 1 \\\\
\n -4x – 2y &=& -2 \\end{array}\\right. \\]<\/p>\n

\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\uff0c\\(x = 1\\), \\(y = -1\\)\u304c\u89e3\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u3000\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306f\uff0c\u69d8\u3005\u306a\u5834\u9762\u3067\u767b\u5834\u3059\u308b\u3068\u3066\u3082\u91cd\u8981\u306a\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u305d\u3057\u3066\u305d\u308c\u3060\u3051\u306b\uff0c\u3068\u3066\u3082\u5927\u898f\u6a21\u306a\u3082\u306e\u3092\u6271\u3046\u3053\u3068\u304c\u826f\u304f\u884c\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\uff0c\u5927\u898f\u6a21\u5316\u3057\u3084\u3059\u3044\u3088\u3046\uff0c\u5b9a\u6570\u3084\u5909\u6570\u306f\\(a\\)\u3068\\(x\\)\u3068\u3044\u3046\u4e8c\u3064\u306e\u6587\u5b57\u306b\u5236\u9650\u3057\uff0c\u5927\u898f\u6a21\u5316\u3057\u305f\u6642\u306b\u306f\u5b9a\u6570\u3084\u5909\u6570\u306b\u6dfb\u3048\u5b57\uff08\u4e0b\u4ed8\u304d\u6570\u5b57\uff09\u3092\u3064\u3051\u3066\u533a\u5225\u3059\u308b\u3088\u3046\u306b\u5909\u66f4\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u4e0a\u306e2\u51432\u6b21\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u66f8\u304d\u76f4\u3057\u307e\u3059\u3002<\/p>\n

\\[\\left\\{\\begin{array}{ccc} a_{11}x_1 + a_{12}x_2 &=& b_1 \\\\
\n a_{21}x_1 + a_{22}x_2 &=& b_2 \\end{array}\\right. \\]<\/p>\n

\u3000\u6dfb\u3048\u5b57\u304c\u7570\u306a\u308b\u6587\u5b57\u306f\u9055\u3046\u3082\u306e\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3061\u3087\u3063\u3068\u76ee\u304c\u30c1\u30ab\u30c1\u30ab\u3057\u307e\u3059\u304c\uff0c\u6211\u6162\u3057\u3066\u4e0b\u3055\u3044\u3002<\/p>\n

\u3000\u3055\u3066\uff0c\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u91cd\u8981\u306a\u3068\u3053\u308d\u306f\uff0c\u5909\u6570\u306e\u500b\u6570\u3068\u65b9\u7a0b\u5f0f\u306e\u500b\u6570\u304c\u540c\u3058\u3067\u3042\u308b\u3068\u3053\u308d\u3067\u3059\u30022\u51432\u6b21\u306e\u5834\u5408\u306f\uff0c\u305d\u308c\u305e\u308c\u306e\u65b9\u7a0b\u5f0f\u304c\u76f4\u7dda\u306b\u306a\u3063\u3066\u304a\u308a\uff0c2\u3064\u306e\u76f4\u7dda\u306e\u4ea4\u308f\u308b\u4ea4\u70b9\u304c\u89e3\u3068\u306a\u3063\u3066\u3044\u308b\uff0c\u3068\u3044\u3046\u3053\u3068\u3092\u8003\u3048\u308b\u3068\uff0c\u89e3\u304c\u4e00\u3064\u306b\u5b9a\u307e\u308b\u305f\u3081\u306b\u306f2\u3064\u306e\u65b9\u7a0b\u5f0f\uff1d2\u672c\u306e\u76f4\u7dda\u304c\u5fc5\u8981\u3067\u3042\u308b\u3053\u3068\u306f\u611f\u899a\u7684\u306b\u7406\u89e3\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n

\u3000\u3067\u306f\u5909\u6570\u304c3\u3064\uff0c\u5373\u3061\\(x_1\\), \\(x_2\\), \\(x_3\\)\u306b\u306a\u3063\u305f\u6642\u306f\u3069\u3046\u3067\u3057\u3087\u3046\uff1f\u3000\u3053\u306e\u5834\u5408\uff0c\u65b9\u7a0b\u5f0f\u306f
\n\\[ ax_1 + bx_2 + cx_3 = d \\]
\n\u3068\u3044\u3046\u5f62\u306b\u306a\u308a\u307e\u3059\u306e\u3067\uff0c\u56f3\u5f62\u3068\u3057\u3066\u306f\u5e73\u9762\u3092\u610f\u5473\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u300c\u677f\uff08\u3044\u305f\uff09\u300d\u3067\u3059\u306d\u3002\u4e26\u884c\u3067\u306a\u3044\u300c\u677f1\u300d\u3068\u300c\u677f2\u300d\u304c\u4e8c\u3064\u91cd\u306a\u308b\u3068\u3053\u308d\u306f\u76f4\u7dda\u306b\u306a\u308a\u307e\u3059\u306e\u3067\uff0c\u70b9\u3068\u3057\u3066\u306f\u4e00\u3064\u306b\u7d5e\u308c\u307e\u305b\u3093\u3002\u66f4\u306b\u3082\u3046\u4e00\u3064\u300c\u677f3\u300d\u3092\u6301\u3063\u3066\u304f\u308b\u3068\uff0c\u65e2\u306b\u5b58\u5728\u3057\u3066\u3044\u308b\u300c\u677f1\u300d\u3068\u300c\u677f2\u300d\u304c\u4ea4\u308f\u308b\u300c\u76f4\u7dda12\u300d\u304c\u3053\u306e\u300c\u677f3\u300d\u3068\u3076\u3064\u304b\u308b\u4ea4\u70b9\u304c\u3067\u304d\u307e\u3059\u306e\u3067\uff0c\u3053\u308c\u304c\u89e3\u3068\u3057\u3066\u4e00\u3064\u306b\u5b9a\u307e\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\uff0c\u4e00\u3064\u306e\u89e3\uff1d\u4ea4\u70b9\u304c\u6c7a\u307e\u308b\u306b\u306f\uff0c\u677f\uff1d\u65b9\u7a0b\u5f0f\u306f3\u3064\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u5f93\u3063\u30663\u3064\u306e\u5909\u6570\u306b\u5bfe\u3057\u3066\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306a3\u51433\u6b21\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b\u8a33\u3067\u3059\u3002<\/p>\n

\\[\\left\\{\\begin{array}{ccc} a_{11}x_1 + a_{12}x_2 + a_{13}x_3 &=& b_1 \\\\
\n a_{21}x_1 + a_{22}x_2 + a_{23}x_3 &=& b_2 \\\\
\n a_{31}x_1 + a_{32}x_2 + a_{33}x_3 &=& b_3 \\\\
\n \\end{array}\\right. \\]<\/p>\n

\u3000\u4ee5\u4e0b\u306f\u540c\u69d8\u3067\u3059\u3002\u5909\u6570\u304c4\u3064\u306b\u306a\u308c\u3070\u65b9\u7a0b\u5f0f\u306f4\u672c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u5909\u6570\u304c5\u3064\u306b\u306a\u308c\u3070\u65b9\u7a0b\u5f0f\u306f5\u672c\uff0c\u30fb\u30fb\u30fb\uff0c\u3064\u307e\u308a\uff0c\u5909\u6570\u304c\\(n\\)\u500b\u3042\u308c\u3070\u65b9\u7a0b\u5f0f\u306f\\(n\\)\u672c\u5fc5\u8981\u306b\u306a\u308b\u8a33\u3067\u3059\u3002\u305d\u308c\u3092\u4e0b\u8a18\u306e\u3088\u3046\u306b\u8868\u73fe\u3057\u307e\u3059\u3002<\/p>\n

\\[\\left\\{\\begin{array}{cccc} a_{11}x_1 + a_{12}x_2 + \\cdots + a_{1n}x_n &=& b_1 \\\\
\n a_{21}x_1 + a_{22}x_2 + \\cdots + a_{2n}x_n &=& b_2 \\\\
\n \\cdots & & \\cdots \\\\
\n a_{n1}x_1 + a_{n2}x_2 + \\cdots + a_{nn}x_n &=& b_n \\\\
\n \\end{array}\\right. \\]<\/p>\n

\u3000\u3055\u3089\u306b\u7c21\u7565\u5316\u3057\u3066\u66f8\u304d\u305f\u3044\u3068\u304d\u306b\u306f\uff0c\u4fc2\u6570\\(a_{ij}\\)\uff0c\u5909\u6570(\u89e3)\\(x_i\\)\uff0c\u53f3\u8fba\u306e\u5b9a\u6570\u9805\\(b_i\\)\u3092\u30d0\u30e9\u30b7\u3066
\n\u305d\u308c\u305e\u308c\u306e\u30ab\u30bf\u30de\u30ea\u3092\uff0c\\(A\\), \\(\\mathbf{x}\\)\uff0c\\(\\mathbf{b}\\)\u3068\u8868\u8a18\u3057<\/p>\n

\\[ A = \\left[\\begin{array}{cccc}
\n a_{11} & a_{12} & \\cdots & a_{1n} \\\\
\n a_{21} & a_{22} & \\cdots & a_{2n} \\\\
\n \\vdots & \\vdots & & \\vdots \\\\
\n a_{n1} & a_{n2} & \\cdots & a_{nn}
\n\\end{array}\\right],\\ \\mathbf{x} = \\left[\\begin{array}{c}
\n x_1 \\\\
\n x_2 \\\\
\n \\vdots \\\\
\n x_n
\n\\end{array}\\right],\\ \\mathbf{b} = \\left[\\begin{array}{c}
\n b_1 \\\\
\n b_2 \\\\
\n \\vdots \\\\
\n b_n
\n\\end{array}\\right] \\]<\/p>\n

\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u884c\u306e\u6570\u5f0f\u3067\u8868\u73fe\u3057\u307e\u3059\u3002<\/p>\n

\\[ A\\mathbf{x} = \\mathbf{b} \\]<\/p>\n

\u3053\u3053\u3067\\(A\\)\u3092\u4fc2\u6570\u304b\u3089\u306a\u308b\u300c\u884c\u5217(matrix)\u300d\uff0c\\(\\mathbf{x}\\)\u3092\u300c\u89e3\u30d9\u30af\u30c8\u30eb(vector)\u300d\uff0c\\(\\mathbf{b}\\)\u3092\u300c\u5b9a\u6570\u30d9\u30af\u30c8\u30eb\u300d\u3068\u547c\u3073\u307e\u3059\u3002\u6700\u521d\u306b\u4f8b\u793a\u3057\u305f2\u51432\u6b21\u65b9\u7a0b\u5f0f<\/p>\n

\\[\\left\\{\\begin{array}{ccc} 3x_1 + 2x_2 &=& 1 \\\\
\n -4x_1 – 2x_2 &=& -2 \\end{array}\\right. \\]<\/p>\n

\u306b\u5bfe\u3057\u3066\u306f
\n\\[ A = \\left[\\begin{array}{cc} 3 & 2 \\\\
\n-4 & -2 \\end{array}\\right],\\ \\mathbf{x} = \\left[\\begin{array}{c}
\n x_1 \\\\
\n x_2
\n\\end{array}\\right],\\ \\mathbf{b} = \\left[\\begin{array}{c}
\n 1 \\\\
\n -2
\n\\end{array}\\right] \\]
\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n

3.\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u304d\u65b9<\/strong><\/p>\n

\u3000\u3055\u3066\uff0c\u3067\u306f\u5927\u898f\u6a21\u306a\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u3069\u3046\u89e3\u3044\u3066\u3044\u304f\u304b\uff1f\u3000\u305d\u306e\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f\u5927\u5b66\u5b66\u90e8\u306e\u300c\u7dda\u5f62\u4ee3\u6570\u300d\u3068\u3044\u3046\u79d1\u76ee\u3067\u7fd2\u3046\u5185\u5bb9\u306b\u306a\u308b\u306e\u3067\uff0c\u305d\u306e\u30a8\u30c3\u30bb\u30f3\u30b9\u3060\u3051\u3092\u8ff0\u3079\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n

\u3000\u307e\u305a\uff0c\u7c21\u5358\u306a2\u51432\u6b21\u306e\u4f8b\u3067\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u809d\u5fc3\u306a\u306e\u306f\uff0c\u300c\u81ea\u52d5\u7684\u306b\u89e3\u3051\u308b\u5f62\u306b\u65b9\u7a0b\u5f0f\u3092\u5909\u5f62\u3059\u308b\u300d\u2192\u300c\u81ea\u52d5\u7684\u306b\u89e3\u3044\u3066\u3057\u307e\u3046\u300d\u3068\u3044\u3046\u624b\u9806\u3092\u8e0f\u3080\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u4f8b\u3048\u3070\\(u_{21} = 0\\)\u3067\u3042\u308c\u3070<\/p>\n

\u3000\\[\\left\\{\\begin{array}{rcl} u_{11}x_1 + u_{12} x_2 &=& y_1 \\\\
\n u_{22} x_2 &=& y_2 \\end{array}\\right. \\]<\/p>\n

\u3068\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u306e\u3067\uff0c\u4e0b\u306e\u5f0f\u304b\u3089\u9806\u306b\\(x_2 = y_2 \/ u_{22} \\)\u3068\u3057\u3066\\(x_2\\)\u3092\u6c42\u3081\uff0c\u6b21\u306b\u305d\u308c\u3092\u4e0a\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\\(x_1 = u_{12} x_2 \/ u_{11}\\)\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\uff0c\u4e00\u756a\u4e0b\u306e\u5f0f\u304c\u5909\u6570\u304c\u4e00\u3064\u3060\u3051\u306e\u65b9\u7a0b\u5f0f\u306b\u306a\u3063\u305f\u683c\u597d\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306f\uff0c\u4fc2\u6570\u884c\u5217\\(A\\)\u304c\u4e0a\u4e09\u89d2\u884c\u5217\\(U\\)\uff0c\u5373\u3061
\n\\[ U = \\left[\\begin{array}{cc}
\n u_{11} & u_{12} \\\\
\n 0 & u_{22}
\n\\end{array}\\right] \\]
\n\u3092\u7528\u3044\u3066
\n\\begin{equation}
\nU\\mathbf{x} = \\mathbf{y} \\label{eqn:upper_triangle}
\n\\end{equation}
\n\u3068\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u4e0a\u4e09\u89d2\u884c\u5217\u3092\u4fc2\u6570\u3068\u3057\u3066\u6301\u3064\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u4e0b\u306e\u65b9\u304b\u3089\u89e3\u3044\u3066\u3044\u304f\u65b9\u6cd5\u3092\u300c\u5f8c\u9000\u4ee3\u5165\u300d\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n

\u3000\u540c\u69d8\u306b\\(l_{11} = l_{22} = 1\\)\u304b\u3064\\(l_{12} = 0\\)\u3067\u3042\u308c\u3070<\/p>\n

\\[\\left\\{\\begin{array}{rcl} y_1 \\phantom{+ u_{12}y_2} &=& b_1 \\\\
\n l_{21}y_1 + y_2 &=& b_2 \\end{array}\\right. \\]<\/p>\n

\u3068\u8868\u73fe\u3067\u304d\u307e\u3059\u306e\u3067\uff0c\u3053\u308c\u3082\u4e0a\u304b\u3089\u9806\u306b\\(y_1 = b_1\\)\uff0c\u6b21\u306b\\(y_2 = b_2 – l_{21}y_1\\)\u3068\u3057\u3066\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u4fc2\u6570\u884c\u5217\u306f\u4e0b\u4e09\u89d2\u884c\u5217\\(L\\)\uff0c\u5373\u3061
\n\\[ L = \\left[\\begin{array}{cc}
\n 1 & 0 \\\\
\n l_{21} & 1
\n\\end{array}\\right] \\]
\n\u3092\u7528\u3044\u3066
\n\\begin{equation}
\nL \\mathbf{y} = \\mathbf{b}
\n\\end{equation}
\n\u3068\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u4e0b\u4e09\u89d2\u884c\u5217\u3092\u4fc2\u6570\u3068\u3057\u3066\u6301\u3064\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u4e0a\u306e\u65b9\u304b\u3089\u89e3\u3044\u3066\u3044\u304f\u65b9\u6cd5\u3092\u300c\u524d\u9032\u4ee3\u5165\u300d\u3068\u547c\u3073\u307e\u3059\u3002<\/p>\n

\u3000\u7d50\u8ad6\u3092\u5148\u306b\u8ff0\u3079\u308b\u3068\uff0c\u4e0a\u8a182\u3064\u306e\u5f62\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u5c0e\u3044\u3066\uff0c\u6b21\u306e\u3088\u3046\u306b\u3057\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n

    \n
  1. [LU\u5206\u89e3]\u3000 \u4fc2\u6570\u884c\u5217\\(A\\)\u304b\u3089\u4e0b\u4e09\u89d2\u884c\u5217\\(L\\)\u3068\u4e0a\u4e09\u89d2\u884c\u5217\\(U\\)\u3092\u6c42\u3081\u308b(\u5b9f\u306f\\(A = LU\\)\u3068\u3044\u3046\u95a2\u4fc2\u306b\u306a\u308a\u307e\u3059)<\/li>\n
  2. [\u524d\u9032\u4ee3\u5165] \\(L\\mathbf{y} = \\mathbf{b}\\)\u3092\\(\\mathbf{y}\\)\u306b\u3064\u3044\u3066\u89e3\u304f<\/li>\n
  3. [\u5f8c\u9000\u4ee3\u5165] \\(U\\mathbf{x} = \\mathbf{y}\\)\u3092\\(\\mathbf{x}\\)\u306b\u3064\u3044\u3066\u89e3\u304f<\/li>\n<\/ol>\n

    \u3000\u5b9f\u969b\u306b
    \n\\[\\left\\{\\begin{array}{ccc} 3x_1 + 2x_2 &=& 1 \\\\
    \n -4x_1 – 2x_2 &=& -2 \\end{array}\\right. \\]
    \n\u3067LU\u5206\u89e3\u2192\u524d\u9032\u4ee3\u5165\u2192\u5f8c\u9000\u4ee3\u5165\u3092\u884c\u3063\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n

    \u3000\u307e\u305aLU\u5206\u89e3\u3067\u3059\u3002
    \n\\[ A = \\left[\\begin{array}{cc}
    \n 3 & 2 \\\\
    \n -4 & -2
    \n\\end{array}\\right] \\]
    \n\u3092\uff0c\u884c\uff08\u6a2a\u4e00\u5217\uff09\u3092\u3072\u3068\u307e\u3068\u3081\u306b\u8db3\u3057\u305f\u308a\u5f15\u3044\u305f\u308a\u5b9a\u6570\u500d\u3057\u305f\u308a\u3057\u3066\uff0c\u4e0a\u4e09\u89d2\u884c\u5217\\(U\\)\u306b\u3057\u307e\u3059\u3002
    \n\\[ \\left[\\begin{array}{cc}
    \n 3 & 2 \\\\
    \n -4 & -2
    \n\\end{array}\\right] \\Rightarrow \\left[\\begin{array}{cc}
    \n 3 & 2 \\\\
    \n -4 – (-4)\/3\\times 3 & -2 – (-4)\/3\\times 2
    \n\\end{array}\\right] = \\left[\\begin{array}{cc}
    \n 3 & 2\\\\
    \n 0 & 2\/3 \\\\
    \n\\end{array}\\right] = U \\]
    \n\u7b2c1\u884c\u76ee\u306b\\((-4)\/3\\)\u3092\u639b\u3051\u3066\uff0c\u7b2c2\u884c\u76ee\u304b\u3089\u5f15\u3044\u3066\u3044\u308b\u308f\u3051\u3067\u3059\u3002\u3053\u3046\u3057\u3066\\(a_{21}\\Rightarrow 0\\)\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u5b9f\u306f\u3053\u306e\u6642\uff0c\u4e0b\u4e09\u89d2\u884c\u5217\\(L\\)\u3082\u81ea\u52d5\u7684\u306b\u6c42\u3081\u3089\u308c\u3066\u304a\u308a\uff0c
    \n\\[ L = \\left[\\begin{array}{cc}
    \n 1 & 0 \\\\
    \n -4\/3 & 1
    \n\\end{array}\\right] \\]
    \n\u306b\u306a\u308a\u307e\u3059\u3002\u5b9f\u306f\\(a_{21} \/ a_{11} = -4 \/ 3\\)\u3092\u8a08\u7b97\u3057\u305f\u3060\u3051\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

    \u3000\u3053\u3046\u3057\u3066\u51fa\u3066\u304d\u305f\\(L, U\\)\u3092\u7528\u3044\u3066
    \n\\[ L\\mathbf{y} = \\mathbf{b} \\Longleftrightarrow \\left[\\begin{array}{cc}
    \n 1 & 0 \\\\
    \n -4\/3 & 1
    \n\\end{array}\\right] \\left[\\begin{array}{c}
    \n y_1 \\\\
    \n y_2
    \n\\end{array}\\right] = \\left[\\begin{array}{c}
    \n 1 \\\\
    \n -2
    \n\\end{array}\\right] \\]
    \n\u3092\u89e3\u3044\u3066\\[ \\mathbf{y} = \\left[\\begin{array}{c}
    \n 1 \\\\
    \n -2\/3
    \n\\end{array}\\right] \\] \u3092\u6c42\u3081\uff0c\u6b21\u306b
    \n\\[ U\\mathbf{x} = \\mathbf{y} \\Longleftrightarrow \\left[\\begin{array}{cc}
    \n 3 & 2 \\\\
    \n 0 & 2\/3
    \n\\end{array}\\right] \\left[\\begin{array}{c}
    \n x_1 \\\\
    \n x_2
    \n\\end{array}\\right] = \\left[\\begin{array}{c}
    \n 1 \\\\
    \n -2\/3
    \n\\end{array}\\right] \\]
    \n\u3092\u89e3\u3044\u3066\\[ \\mathbf{x} = \\left[\\begin{array}{c}
    \n 1 \\\\
    \n -1
    \n\\end{array}\\right] \\] \u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n

    \u3000\u3053\u306e\u65b9\u6cd5\u306f\\(n\\)\u5143\\(n\\)\u6b21\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306b\u306a\u3063\u3066\u3082\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\uff0c\u8a08\u7b97\u306e\u624b\u9593\u304c\u81a8\u5927\u306b\u5897\u3048\u3066\u3044\u304d\u307e\u3059\u3002\u5b9f\u969b\uff0cLU\u5206\u89e3\u306f
    \n\\[ A = \\left[\\begin{array}{cccc}
    \n a_{11} & a_{12} & \\cdots & a_{1n} \\\\
    \n a_{21} & a_{22} & \\cdots & a_{2n} \\\\
    \n \\vdots & \\vdots & & \\vdots \\\\
    \n a_{n1} & a_{n2} & \\cdots & a_{nn}
    \n\\end{array}\\right]\\]
    \n\\[\\Rightarrow \\left[\\begin{array}{cccc}
    \n a_{11} & a_{12} & \\cdots & a_{1n} \\\\
    \n a_{21}\/a_{11} & a_{22} – a_{21}\/a_{11}\\times a_{12} & \\cdots & a_{2n} – a_{21}\/a_{11}\\times a_{1n} \\\\
    \n \\vdots & \\vdots & & \\vdots \\\\
    \n a_{n1}\/a_{11} & a_{n2} – a_{n1}\/a_{11}\\times a_{12} & \\cdots & a_{nn} – a_{n1}\/a_{11}\\times a_{1n}
    \n\\end{array}\\right]\\]
    \n\\[\\Rightarrow \\cdots \\Rightarrow \\left[\\begin{array}{cccc}
    \n a_{11} & a_{12} & \\cdots & a_{1n} \\\\
    \n a^{(1)}_{21} & a^{(2)}_{22} & \\cdots & a^{(2)}_{2n} \\\\
    \n \\vdots & \\vdots & & \\vdots \\\\
    \n a^{(1)}_{n1} & a^{(2)}_{n2} & \\cdots & a^{(n-1)}_{nn}
    \n\\end{array}\\right]\\]
    \n\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u904e\u7a0b\u3092\u56f3\u793a\u3059\u308b\u3068\u4e0b\u8a18\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

    \"lu\"<\/a><\/p>\n

    \u9ed2\u304f\u5857\u308a\u3064\u3076\u3057\u305f\u56db\u89d2\u90e8\u5206\u306f
    \n\\[ a^{(i-1)}_{ji} \/ a^{(i-1)}_{ii}\\ (j = i + 1, …, n) \\]
    \n\u306e\u8a08\u7b97\u3092\u884c\u3044\uff0c\u7070\u8272\u306e\u90e8\u5206\u306f
    \n\\[ a^{(i-1)}_{jk} – a^{(i-1)}_{ji} \/ a^{(i-1)}_{ii} \\times a^{(i-1)}_{ik}\\ (j, k = i+1, …, n) \\]
    \n\u306e\u8a08\u7b97\u3092\u884c\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n

    \u9ed2\u3044\u56db\u89d2\u90e8\u5206\u306f\\[ (n-1) + (n-2) + \\cdots + 2 + 1 \\]\u500b\u3068\u306a\u308a\uff0c\u7070\u8272\u306e\u90e8\u5206\u306f\\[ (n-1)^2 + (n-2)^2 + \\cdots + 2 + 1 \\]\u500b\u3068\u306a\u308a\uff0c\u305d\u308c\u305e\u308c\uff11\u56de\u305a\u3064\u306e\u5272\u7b97\u3068\u639b\u7b97\u304c\u5165\u3063\u3066\u3044\u307e\u3059\u306e\u3067\uff0c\u3053\u306e\u5272\u7b97\u3068\u639b\u7b97\u306e\u56de\u6570\u3060\u3051\u3067\u3082
    \n\\[ \\sum^{n-1}_{i=1} i(i + 1) = \\frac{n(n^2 – 1)}{3} \\]
    \n\u3068\u306a\u308a\u307e\u3059\u304b\u3089\uff0c\u6700\u7d42\u7684\u306b\u306f\\(O(n^3)\\)\u306e\u624b\u9593\u304c\u304b\u304b\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\\(n\\)\u304c10\u500d\u305a\u3064\u5897\u3048\u3066\u3044\u304f\u3068\u304d\uff0c\\(O(n)\\)\u306e\u8a08\u7b97\u304c10\u79d2\uff0c100\u79d2\uff0c1000\u79d2\u30fb\u30fb\u30fb\u3068\u5897\u3048\u3066\u3044\u304f\u3068\u3059\u308b\u3068\uff0c\\(O(n^3)\\)\u306f1000\u79d2\uff0c1000000\u79d2, 1000000000\u79d2\u30fb\u30fb\u30fb\u306e\u3088\u3046\u306b\u5897\u3048\u3066\u3044\u304d\u307e\u3059\u3002\u8a08\u7b97\u6642\u9593\u306e\u5897\u3048\u65b9\u304c1000\u500d\u306b\u306a\u3063\u3066\u3044\u304f\u308f\u3051\u3067\u3059\u3002<\/p>\n

    \u3000\u3053\u3046\u3057\u3066\\(L, U\\)\u306f
    \n\\[ L = \\left[\\begin{array}{cccc}
    \n 1 & 0 & \\cdots & 0 \\\\
    \n a^{(1)}_{21} & 1 & \\cdots & \\vdots \\\\
    \n \\vdots & \\ddots & \\ddots & 0 \\\\
    \n a^{(1)}_{n1} & \\cdots & a^{(n-1)}_{n,n-1} & 1
    \n\\end{array}\\right],\\ U = \\left[\\begin{array}{cccc}
    \n a_{11} & a_{12} & \\cdots & a_{1n} \\\\
    \n 0 & a^{(2)}_{22} & \\cdots & a^{(2)}_{2n} \\\\
    \n \\vdots & \\ddots & & \\vdots \\\\
    \n 0 & \\cdots & 0 & a^{(n-1)}_{nn}
    \n\\end{array}\\right] \\]
    \n\u3068\u3057\u3066\u5f97\u3089\u308c\u307e\u3059\u306e\u3067\uff0c\u524d\u9032\u4ee3\u5165\u306f\\(L\\mathbf{y} = \\mathbf{b}\\)\u3092\u89e3\u3044\u3066
    \n\t\\begin{align*}
    \n\t\ty_1 &:= b_1 \\\\
    \n\t\ty_2 &:= b_2 – a^{(1)}_{21} y_1 \\\\
    \n\t\t& \\vdots \\\\
    \n\t\ty_{n-1} &:= b_{n-1} – \\sum^{n-2}_{j=1} a^{(j)}_{n-1,j}y_j \\\\
    \n\t\ty_n &:= b_n – \\sum^{n-1}_{j=1} a^{(j)}_{nj}y_j
    \n\t\\end{align*}
    \n\u3068\u306a\u308a\uff0c\u5f8c\u9000\u4ee3\u5165\u306f\\(U \\mathbf{x} = \\mathbf{y}\\)\u3092\u89e3\u3044\u3066
    \n\t\\begin{align*}
    \n\t\tx_n &:= \\frac{y_n}{a^{(n-1)}_{nn}} \\\\
    \n\t\tx_{n-1} &:= \\frac{y_{n-1} – a^{(n-2)}_{n-1,n} x_n}{a^{(n-2)}_{n-1, n-1}} \\\\
    \n\t\t& \\vdots \\\\
    \n\t\tx_2 &:= \\frac{y_2 – \\sum^{n}_{j=3} a^{(1)}_{2j} x_j}{a^{(1)}_{22}} \\\\
    \n\t\tx_1 &:= \\frac{y_1 – \\sum^{n}_{j=2} a_{1j} x_j}{a_{11}}
    \n\t\\end{align*}
    \n\u3068\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

    \u3000\u5f93\u3063\u3066\uff0c\u524d\u9032\u4ee3\u5165\uff0c\u5f8c\u9000\u4ee3\u5165\u306e\u624b\u9593\u306f\\(O(n^2)\\)\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

    4. \u4e26\u5217\u3067\u8a08\u7b97\u3059\u308b\u306b\u306f\uff1f<\/strong><\/p>\n

    \u3000\u3055\u3066\uff0c\u3053\u306e\u3088\u3046\u306b\u5927\u898f\u6a21\u5316\u3057\u305f\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u73fe\u5728\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u4e0a\u3067\u9ad8\u901f\u306b\u89e3\u304f\u305f\u3081\u306b\u306f\uff0cLU\u5206\u89e3\uff0c\u524d\u9032\u4ee3\u5165\uff0c\u5f8c\u9000\u4ee3\u5165\u306e\u8a08\u7b97\u3092\u4e26\u5217\u5316\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

    \u3000LU\u5206\u89e3\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u4e26\u5217\u5316\u3057\u307e\u3059\u3002\u8272\u5206\u3051\u3057\u305f\u90e8\u5206\u3092\u5404\u30b9\u30ec\u30c3\u30c9\u306b\u5206\u914d\u3057\u3066\u4e26\u5217\u306b\u8a08\u7b97\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n

    \"parallel_lu\"<\/a><\/p>\n

    \u3000\u524d\u9032\u4ee3\u5165\uff0c\u5f8c\u9000\u4ee3\u5165\u3082\u4e0b\u8a18\u306e\u3088\u3046\u306b\u4e26\u5217\u5316\u3057\u307e\u3059\u3002<\/p>\n

    \"parallel_subst\"<\/a><\/p>\n

    \u3000LU\u5206\u89e3\u3082\u524d\u9032\u4ee3\u5165\uff0c\u5f8c\u9000\u4ee3\u5165\u3082\uff0c\u8a08\u7b97\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u8a08\u7b97\u91cf\u304c\u6e1b\u308a\uff0c\u7d50\u679c\u7684\u306b\u3060\u3093\u3060\u3093\u4e26\u5217\u5316\u52b9\u7387\u304c\u843d\u3061\u3066\u3044\u304d\u307e\u3059\u304c\uff0c\u3053\u308c\u4ee5\u4e0a\u306e\u826f\u3044\u624b\u6bb5\u306f\u306a\u304b\u306a\u304b\u898b\u3064\u304b\u3089\u306a\u3044\u3068\u3044\u3046\u306e\u304c\u73fe\u72b6\u3067\u3059\u3002\u3057\u304b\u3057\u3053\u306e\u3088\u3046\u306b\u4e26\u5217\u5316\u3059\u308b\u3053\u3068\u3067\uff0c\u30de\u30eb\u30c1\u30b3\u30a2CPU\u74b0\u5883\u30fbGPU\u74b0\u5883\u3067\u306f\u9ad8\u901f\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u5b9f\u969b\u306b12\u30b3\u30a2CPU\u3068Tesla K20\u3068\u3044\u3046GPU\u3092\u7a4d\u3093\u3060\u30ef\u30fc\u30af\u30b9\u30c6\u30fc\u30b7\u30e7\u30f3\u74b0\u5883\u3067\u89e3\u3044\u305f\u7d50\u679c\u304c\u4e0b\u8a18\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

    \"dsgesv_cpu_gpu\"<\/a><\/p>\n

    \u3000\u6700\u5927\\(n = 8192\\)\u307e\u3067\u306e\u898f\u6a21\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u8aac\u3044\u305f\u6642\u306e\u8a08\u7b97\u6642\u9593\u3068\u8a08\u7b97\u306b\u4f34\u3046\u4e38\u3081\u8aa4\u5dee\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u3044\u307e\u3059\u3002GPU\u306e\u65b9\u304c\u5727\u5012\u7684\u306b\u9ad8\u901f\u306b\u8a08\u7b97\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n

    5. \u307e\u3068\u3081<\/strong><\/p>\n

    \u3000\u99c6\u3051\u8db3\u3067\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u304c\uff0c\u3053\u3053\u3067\u8aac\u660e\u3057\u305f\u5927\u898f\u6a21\u306a\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092LU\u5206\u89e3\u30fb\u524d\u9032\u4ee3\u5165\u30fb\u5f8c\u9000\u4ee3\u5165\u3092\u4f7f\u3063\u3066\u89e3\u304f\u65b9\u6cd5\u306f\u76f4\u63a5\u6cd5(direct method)\u3068\u547c\u3070\u308c\uff0cLinpack\uff08\u30ea\u30f3\u30d1\u30c3\u30af\uff09\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u30c6\u30b9\u30c8\u3068\u547c\u3070\u308c\u308b\uff0c\u30b9\u30fc\u30d1\u30fc\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u901f\u5ea6\u6bd4\u8f03\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002Top500\u3068\u3044\u3046\u30b5\u30a4\u30c8<\/a>\u306b\u306f\uff0c\u6bce\u5e74\u534a\u671f\u3054\u3068\u306b\u4e16\u754c\u4e2d\u306e\u30b9\u30fc\u30d1\u30fc\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306eLinpack\u30c6\u30b9\u30c8\u306e\u7d50\u679c\u306b\u57fa\u3065\u3044\u305f\u30e9\u30f3\u30ad\u30f3\u30b0\u304c\u63b2\u8f09\u3055\u308c\u3066\u304a\u308a\uff0c2015\u5e749\u6708\u73fe\u5728\u306e\u30ca\u30f3\u30d0\u30fc\u30ef\u30f3\u306f\u4e2d\u56fd\u306b\u3042\u308a\u307e\u3059\u3002\u65e5\u672c\u3067\u306f\u795e\u6238\u306b\u3042\u308b\u300c\u4eac\uff08\u30b1\u30a4\uff09\u300d\u3068\u3044\u3046\u30b9\u30fc\u30d1\u30fc\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u304c\u6700\u9ad8\u901f\u3067\uff0c\u73fe\u5728\u306f\u4e16\u754c\u7b2c4\u4f4d\u306b\u5f8c\u9000\u3057\u307e\u3057\u305f\u3002<\/p>\n

    \u3000\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u306e\u6027\u80fd\u8a55\u4fa1\u306e\u305f\u3081\u306eLinpack\u30c6\u30b9\u30c8\u306f\uff0c\u7686\u3055\u3093\u304c\u4e2d\u5b66\u6821\u3067\u7fd2\u3046\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306e\u62e1\u5927\u7248\u3067\u884c\u308f\u308c\u3066\u304a\u308a\uff0c\u305d\u308c\u3089\u306f\\(O(n^3)\\)\u306e\u51e6\u7406\u6642\u9593\u3092\u8981\u3059\u308b\u3082\u306e\u3067\u3042\u308b\uff0c\u3068\u3044\u3046\u3053\u3068\u3092\u7406\u89e3\u3057\u3066\u3082\u3089\u3048\u3070\u5e78\u3044\u3067\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u3000\u3053\u308c\u306f\u6a21\u64ec\u8b1b\u7fa9\u300c\u6570\u5b66\u3068\u8a08\u7b97\u3000\uff5e\u7406\u8ad6\u3068\u5b9f\u8df5\uff5e\u300d\u306e\u7d9a\u304d\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305a\u305d\u3061\u3089\u3092\u8aad\u3093\u3067\u9802\u3044\u3066\u304b\u3089\uff0c\u3053\u3061\u3089\u306e\u6587\u7ae0\u306b\u53d6\u308a\u7d44\u3093\u3067\u4e0b\u3055\u3044\u3002 1. \u5927\u898f\u6a21\u8a08\u7b97\u3068\u306f\uff1f \u3000\u5927\u898f\u6a21\u8a08\u7b97\u3068\u306f\uff0c\u73fe\u5728\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u304c\u5b9f\u884c\u3059\u308b\u306b\u969b\u3057\uff0c\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092 … <\/p>\n

    “[\u6a21\u64ec\u8b1b\u7fa92] \u5927\u898f\u6a21\u8a08\u7b97\u3068CPU\uff06GPU” 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\u3000\u6570\u5b66\uff08\uff1d\u7406\u8ad6\uff09\u3068\u8a08\u7b97\uff08\uff1d\u5b9f\u8df5\uff09\u306f\u5168\u304f\u6027\u8cea\u306e\u7570\u306a\u308b\u3082\u306e\u3067\uff0c\u8a08\u7b97\u306e\u52b9\u7387\u6027\u3084\u6b63\u78ba\u6027\u3092\u8ffd\u53ca\u3059\u308b\u3068\u6570\u5b66\u2026","rel":"","context":"\u30a8\u30c3\u30bb\u30a4","block_context":{"text":"\u30a8\u30c3\u30bb\u30a4","link":"https:\/\/kd-tklab.na-inet.jp\/?cat=7"},"img":{"alt_text":"basis_computing1","src":"https:\/\/i0.wp.com\/cs-tklab.na-inet.jp\/blog\/wp-content\/uploads\/2015\/05\/basis_computing1-300x195.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":2493,"url":"https:\/\/kd-tklab.na-inet.jp\/?p=2493","url_meta":{"origin":586,"position":1},"title":"\u9ad8\u6027\u80fd\u8a08\u7b97\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0","author":"T.Kouya","date":"2023\u5e747\u670811\u65e5","format":false,"excerpt":"\u5e78\u8c37\u667a\u7d00 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\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u8a08\u7b97\u306f\u6b63\u3057\u304f\u306a\u3044\uff01","author":"T.Kouya","date":"2017\u5e749\u67085\u65e5","format":false,"excerpt":"\u30aa\u30fc\u30d7\u30f3\u30ad\u30e3\u30f3\u30d1\u30b9\u6a21\u64ec\u8b1b\u7fa9 \u300c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u8a08\u7b97\u306f\u6b63\u3057\u304f\u306a\u3044\uff01\u300d \u9759\u5ca1\u7406\u5de5\u79d1\u5927\u5b66\u3000\u60c5\u5831\u5b66\u90e8 \u30b3\u30f3\u30d4\u30e5\u2026","rel":"","context":"\u30a8\u30c3\u30bb\u30a4","block_context":{"text":"\u30a8\u30c3\u30bb\u30a4","link":"https:\/\/kd-tklab.na-inet.jp\/?cat=7"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/cs-tklab.na-inet.jp\/blog\/wp-content\/uploads\/2017\/09\/IMG_3409-_rotation-e1505026985856-225x300.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":2277,"url":"https:\/\/kd-tklab.na-inet.jp\/?p=2277","url_meta":{"origin":586,"position":4},"title":"\u5fdc\u7528\u7dda\u5f62\u4ee3\u6570\u3000\u7b2c8\u56de","author":"T.Kouya","date":"2020\u5e744\u670829\u65e5","format":false,"excerpt":"\u5fdc\u7528\u7dda\u5f62\u4ee3\u6570\u7b2c8\u56de\u3067\u3059\u3002\u3057\u3083\u3079\u308a\u3059\u304e\u30661\u6642\u959322\u5206\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3057\u305f\u304c\uff0c\u300c\u6b63\u898f\u300d\u300c\u76f4\u4ea4\u300d\u300c\u57fa\u5e95\u300d\u300c\u2026","rel":"","context":"\u66f4\u65b0\u60c5\u5831","block_context":{"text":"\u66f4\u65b0\u60c5\u5831","link":"https:\/\/kd-tklab.na-inet.jp\/?cat=2"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":708,"url":"https:\/\/kd-tklab.na-inet.jp\/?p=708","url_meta":{"origin":586,"position":5},"title":"\u300c\u52b9\u7387\u7684\u306a\u624b\u9806\u3068\u306f\uff1f\u300d\u3000\uff1a\u30002\/1 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