{"id":6229,"date":"2026-09-12T22:05:22","date_gmt":"2026-09-12T13:05:22","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=6229"},"modified":"2026-09-12T22:05:22","modified_gmt":"2026-09-12T13:05:22","slug":"5-5_sparse","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/","title":{"rendered":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb"},"content":{"rendered":"\n<h3>5.5.1 \u56fa\u6709\u5024\u554f\u984c\u306e\u6982\u8981<\/h3>\n<h4>5.5.1.1 \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c<\/h4>\n<p>n x n \u884c\u5217 \\(A\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u3092\u6e80\u305f\u3059 \\(\\lambda\\) \u3092\u56fa\u6709\u5024, \\(x\\) \u3092\u305d\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3046.<br \/>\n\\[<br \/>\nAx = \\lambda x<br \/>\n\\]\n\u56fa\u6709\u5024\u304a\u3088\u3073 (\u5fc5\u8981\u306b\u5fdc\u3058\u3066) \u305d\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u308b\u554f\u984c\u3092\u56fa\u6709\u5024\u554f\u984c\u3068\u3044\u3046 (\u4e0b\u306e\u4e00\u822c\u5316\u56fa\u6709\u5024\u554f\u984c\u3068\u533a\u5225\u3059\u308b\u305f\u3081\u306b\u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c\u3068\u3088\u3076\u3053\u3068\u304c\u3042\u308b). \u56fa\u6709\u5024\u306f\u91cd\u8907\u3092\u542b\u3081\u3066 n \u500b\u5b58\u5728\u3059\u308b\u304c, \u884c\u5217 \\(A\\) \u304c\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306b\u306f\u56fa\u6709\u5024\u306f\u5b9f\u6570\u3067, \u884c\u5217 \\(A\\) \u304c\u975e\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306b\u306f\u56fa\u6709\u5024\u306f\u4e00\u822c\u306b\u8907\u7d20\u6570\u3067\u3042\u308b. \u5b9f\u975e\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306b\u306f\u8907\u7d20\u56fa\u6709\u5024\u306f\u5171\u5f79\u5bfe\u3068\u3057\u3066\u73fe\u308c\u308b. \u56fa\u6709\u5024\u305d\u308c\u305e\u308c\u306b\u306f\u5bfe\u5fdc\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308b. \u5fdc\u7528\u4e0a\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u304c\u5fc5\u8981\u306a\u5834\u5408\u3068\u4e00\u90e8\u306e\u56fa\u6709\u5024 (\u4f8b\u3048\u3070, \u5c0f\u3055\u3044\u65b9\u306e\u6570\u500b\u306a\u3069) \u3060\u3051\u304c\u5fc5\u8981\u306a\u5834\u5408\u304c\u3042\u308b. \u307e\u305f, \u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u4e21\u65b9\u304c\u5fc5\u8981\u306a\u5834\u5408\u3068\u56fa\u6709\u5024\u3060\u3051\u304c\u5fc5\u8981\u306a\u5834\u5408\u304c\u3042\u308b.<\/p>\n<h4>5.5.1.2 \u4e00\u822c\u5316\u56fa\u6709\u5024\u554f\u984c<\/h4>\n<p>n x n \u884c\u5217\u306e\u30da\u30a2 \\((A, B)\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u3092\u6e80\u305f\u3059 \\(\\lambda\\) \u3092\u4e00\u822c\u5316\u56fa\u6709\u5024, \\(x\\) \u3092\u305d\u306e\u4e00\u822c\u5316\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3046.<br \/>\n\\[<br \/>\nAx = \\lambda Bx<br \/>\n\\]\n\u5fdc\u7528\u306b\u3088\u3063\u3066\u306f\u4e0a\u5f0f\u306e\u3088\u3046\u306a\u5f62\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u56fa\u6709\u5024\u554f\u984c\u304c\u3042\u308a, \u4e00\u822c\u5316\u56fa\u6709\u5024\u554f\u984c\u3068\u3088\u3070\u308c\u308b.<\/p>\n<h3>5.5.2 \u5927\u898f\u6a21\u758e\u884c\u5217\u7528\u306e\u89e3\u6cd5<\/h3>\n<p>\u5bc6\u884c\u5217 (\u5c0f\u898f\u6a21\u306a\u884c\u5217) \u3067\u306f\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u308b\u89e3\u6cd5\u306f\u4e00\u822c\u7684\u3067\u3042\u308b. \u3057\u304b\u3057, \u3053\u3053\u3067\u6271\u3046\u5927\u898f\u6a21\u758e\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u306e\u5834\u5408\u306b\u306f, \u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u5b9f\u969b\u4e0a\u56f0\u96e3\u3067, \u5fdc\u7528\u4e0a\u3082\u4e00\u90e8\u306e\u56fa\u6709\u5024\u3042\u308b\u3044\u306f\u4e00\u90e8\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3060\u3051\u3067\u5341\u5206\u306a\u5834\u5408\u304c\u591a\u3044.<\/p>\n<p>\u305d\u306e\u3088\u3046\u306a\u5927\u898f\u6a21\u758e\u884c\u5217\u7528\u306e\u89e3\u6cd5\u3068\u3057\u3066\u306f\u3079\u304d\u4e57\u6cd5\u3092\u4f7f\u3046\u3053\u3068\u3082\u3067\u304d\u308b\u304c, \u4e00\u822c\u7684\u306b\u306f\u3079\u304d\u4e57\u6cd5\u3088\u308a\u3082\u53ce\u675f\u304c\u901f\u3044\u5c04\u5f71\u6cd5\u304c\u4f7f\u308f\u308c\u3066\u3044\u308b. \u5c04\u5f71\u6cd5\u306f, \u5c0f\u3055\u306a\u90e8\u5206\u7a7a\u9593\u3078\u306e\u5c04\u5f71\u3092\u4f7f\u3063\u3066\u5927\u898f\u6a21\u56fa\u6709\u5024\u554f\u984c\u3092 (\u305d\u306e\u4e00\u90e8\u306e\u56fa\u6709\u5024\u304b\u3089\u306a\u308b) \u5c0f\u3055\u306a\u56fa\u6709\u5024\u554f\u984c\u3067\u8fd1\u4f3c\u3057\u305d\u308c\u3092\u5bc6\u884c\u5217\u7528\u306e\u89e3\u6cd5\u3067\u89e3\u304f\u3053\u3068\u306b\u3088\u308a\u4e00\u90e8\u306e\u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3067\u3042\u308b. \u90e8\u5206\u7a7a\u9593\u306e\u751f\u6210\u65b9\u6cd5\u306b\u3088\u308a, \u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5, \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5, \u30e4\u30b3\u30d3\u30fb\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u306a\u3069\u304c\u3042\u308b.<\/p>\n<h4>5.5.2.1 \u5c04\u5f71\u6cd5 (\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5)<\/h4>\n<p>n \u00d7 n \u6b63\u5247\u884c\u5217 \\(A\\) \u3068 0 \u3067\u306a\u3044\u30d9\u30af\u30c8\u30eb \\(u\\) \u306e\u30af\u30ea\u30ed\u30d5\u90e8\u5206\u7a7a\u9593 \\(K_k(A; u)\\) \u306b\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u904e\u7a0b\u3092\u9069\u7528\u3059\u308b\u3068\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u305f (5.3.1 \u3092\u53c2\u7167).<br \/>\n\\[<br \/>\nAV_k = V_k H_k + h_{k+1,k}v_{k+1}e_k^T<br \/>\n\\]\n\\(V_k = \\{ v_1, v_2, \\dots, v_k \\}\\) \u306f \\(K_k(A; u)\\) \u306e\u6b63\u898f\u76f4\u4ea4\u57fa\u5e95\u3067\u3042\u308b. k x k \u884c\u5217 \\(H_k\\) \u306f\u4e0a\u30d8\u30c3\u30bb\u30f3\u30d9\u30eb\u30b0\u5f62\u3067\u3042\u308b. \u307e\u305f, \\(e_k = [ 0, 0, &#8230;, 0, 1 ]^T\\) \u3067\u3042\u308b.<\/p>\n<p>\u3053\u3053\u3067, k x k \u884c\u5217 \\(H_k\\) \u306e\u56fa\u6709\u5024\u3092 \\(\\theta\\), \u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092 \\(y\\) \u3068\u3059\u308b\u3068<br \/>\n\\[<br \/>\nH_k y = \\theta y<br \/>\n\\]\n\u3068\u306a\u308a, \\(\\theta\\) \u306f\u30ea\u30c3\u30c4\u5024, \\(y\\) \u306f\u30ea\u30c3\u30c4\u30d9\u30af\u30c8\u30eb\u3068\u3088\u3070\u308c\u308b. \u4e00\u822c\u306b k &lt;&lt; n \u3067\u3042\u308b\u304b\u3089, \u3053\u308c\u3089\u306f\u5bc6\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u3068\u3057\u3066\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b. \u7279\u306b \\(H_k\\) \u306f\u30d8\u30c3\u30bb\u30f3\u30d9\u30eb\u30b0\u5f62\u3067\u3042\u308b\u304b\u3089\u901a\u5e38\u306e\u975e\u5bfe\u79f0\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u3088\u308a\u3082\u697d\u306b\u8a08\u7b97\u3067\u304d\u308b.<\/p>\n<p>\u3053\u306e\u3068\u304d, \\(A\\) \u306e\u56fa\u6709\u5024\u554f\u984c\u306e\u6b8b\u5dee \\(r = Ax &#8211; \\lambda x\\) \u306f \\(x = V_k y\\), \\(\\lambda = \\theta\\) \u3068\u304a\u304f\u3068\u6b21\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b. \u305f\u3060\u3057, \\(y_k\\) \u306f \\(y\\) \u306e k \u756a\u76ee\u306e\u6210\u5206\u3067\u3042\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nr &amp; = Ax &#8211; \\lambda x \\\\<br \/>\n&amp; = AV_k y &#8211; \\theta V_k y \\\\<br \/>\n&amp; = V_k(H_k y &#8211; \\theta y) + h_{k+1,k} y_k v_{k+1} \\\\<br \/>\n&amp; = h_{k+1,k} y_k v_{k+1} \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3059\u306a\u308f\u3061, \\(A\\) \u306e\u56fa\u6709\u5024 \\(\\lambda\\) (\u306e\u4e00\u90e8) \u306f \\(\\theta\\) \u3067, \u307e\u305f, \u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb \\(x\\) \u306f \\(V_k y\\) \u3067\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3066, \u305d\u306e\u3068\u304d\u306e\u6b8b\u5dee\u306f\u4e0a\u5f0f\u306e \\(r\\) \u3067\u8868\u3055\u308c\u308b.<\/p>\n<p>\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u3067\u306f k = 1, 2, &#8230;, m \u3068\u90e8\u5206\u7a7a\u9593\u3092\u62e1\u5f35\u3057\u3066\u3044\u304d k = m \u3067\u4e0d\u5909\u90e8\u5206\u7a7a\u9593\u306b\u9054\u3057\u305f (\u3053\u308c\u4ee5\u4e0a\u62e1\u5f35\u3057\u3066\u3082\u4e00\u6b21\u5f93\u5c5e\u306b\u306a\u308b) \u3068\u3059\u308b\u3068. \\(h_{m+1,m} = 0\\) (\u3059\u306a\u308f\u3061\u6b8b\u5dee \\(r = 0\\)) \u3068\u306a\u308a, \\(\\theta\\) \u3068 \\(y\\) \u306f\u4e38\u3081\u8aa4\u5dee\u304c\u306a\u3051\u308c\u3070\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306b\u4e00\u81f4\u3059\u308b\u3053\u3068\u306b\u306a\u308b. \u5b9f\u969b\u306b\u306f k &lt;&lt; m \u3067\u3082\u5341\u5206\u306a\u8fd1\u4f3c\u56fa\u6709\u5024\u304c\u5f97\u3089\u308c\u308b\u306e\u3067, \u305d\u3053\u3067\u53ce\u675f\u3068\u307f\u306a\u3059.<\/p>\n<h4>5.5.2.2 \u5c04\u5f71\u6cd5 (\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5)<\/h4>\n<p>\u5bfe\u79f0\u884c\u5217\u306b\u5bfe\u3059\u308b\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u306f\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3068\u3088\u3070\u308c, \u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u904e\u7a0b\u306e\u4ee3\u308f\u308a\u306b\u30e9\u30f3\u30c1\u30e7\u30b9\u904e\u7a0b\u3092\u7528\u3044\u308b (5.3.2 \u3092\u53c2\u7167).<\/p>\n<p>\\(H_k\\) \u306f\u5bfe\u79f0\u306a\u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u306b\u306a\u308a, \\(H_k\\) \u306e\u4ee3\u308f\u308a\u306b \\(T_k\\) \u3068\u8868\u3055\u308c\u308b. \u307e\u305f, \u305d\u306e\u8981\u7d20\u306f \\(\\alpha_k (= h_k)\\), \\(\\beta_k (= h_{k-1,k} = h_{k,k-1})\\) \u3068\u66f8\u304b\u308c\u308b\u3053\u3068\u304c\u591a\u3044.<br \/>\n\\[<br \/>\n(V^TAV)_k = V_kT_k + \\beta_{k+1}e_k^T<br \/>\n\\]\n\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u3068\u540c\u69d8\u306b, k x k \u884c\u5217 \\(T_k\\) \u306e\u56fa\u6709\u5024 (\u30ea\u30c3\u30c4\u5024) \u3092 \\(\\theta\\), \u56fa\u6709\u30d9\u30af\u30c8\u30eb (\u30ea\u30c3\u30c4\u30d9\u30af\u30c8\u30eb) \u3092 \\(y\\) \u3068\u3059\u308b. \\(T_k\\) \u306e\u56fa\u6709\u5024\u306f, \u5bfe\u79f0\u306a\u4e09\u91cd\u5bfe\u89d2\u5f62\u306e\u5bc6\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u3068\u3057\u3066\u6bd4\u8f03\u7684\u5bb9\u6613\u306b\u8a08\u7b97\u3067\u304d\u308b.<br \/>\n\\[<br \/>\nT_k y = \\theta y<br \/>\n\\]\nA \u306e\u56fa\u6709\u5024 \\(\\lambda\\) (\u306e\u4e00\u90e8) \u306f \\(\\theta\\) \u3067, \u307e\u305f, \u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb \\(x\\) \u306f \\(V_k y\\) \u3067\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3066, \u305d\u306e\u3068\u304d\u306e\u6b8b\u5dee \\(r\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\nr &amp; = Ax &#8211; \\lambda x \\\\<br \/>\n&amp; = \\beta_{k+1} y_k v_{k+1} \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3067\u306f\u4e09\u9805\u6f38\u5316\u5f0f\u3067\u8a08\u7b97\u3092\u9032\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u304c\u5fc5\u8981\u306a\u3051\u308c\u3070 \\(V_k\\) \u5168\u90e8\u3092\u4fdd\u6301\u3057\u3066\u304a\u304b\u306a\u304f\u3066\u3082\u3088\u3044.<\/p>\n<h4>5.5.2.3 \u5c04\u5f71\u6cd5 (\u30e4\u30b3\u30d3\u30fb\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5)<\/h4>\n<p>A \u306e\u56fa\u6709\u5024\u554f\u984c \\(Ax = \\lambda x\\) \u3092\u8003\u3048, \u73fe\u5728\u6c42\u3081\u3089\u308c\u3066\u3044\u308b\u8fd1\u4f3c\u56fa\u6709\u5024 (\u30ea\u30c3\u30c4\u5024) \u3092 \\(\\theta\\), \u8fd1\u4f3c\u56fa\u6709\u30d9\u30af\u30c8\u30eb (\u30ea\u30c3\u30c4\u30d9\u30af\u30c8\u30eb) \u3092 \\(u\\) \u3068\u3059\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&amp; (V_TAV)y = \\theta \\\\<br \/>\n&amp; u = Vy \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\\(V = \\{ v_1, v_2, \\dots \\}\\) \u306f\u90e8\u5206\u7a7a\u9593\u306e\u6b63\u898f\u76f4\u4ea4\u57fa\u5e95\u3067\u3042\u308b.<\/p>\n<p>\u56fa\u6709\u30d9\u30af\u30c8\u30eb (\u53b3\u5bc6\u89e3) \\(x\\) \u3092\u8fd1\u4f3c\u30d9\u30af\u30c8\u30eb \\(u\\) \u3068\u305d\u308c\u306b\u76f4\u4ea4\u3059\u308b\u4fee\u6b63\u30d9\u30af\u30c8\u30eb \\(t\\) \u306e\u548c\u3067\u8868\u3059.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&amp; x = u + t \\\\<br \/>\n&amp; \u305f\u3060\u3057, \\space t^Hu = 0 \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u306e \\(t\\) \u3092\u7528\u3044\u3066\u90e8\u5206\u7a7a\u9593\u3092\u62e1\u5f35\u3059\u308b (\\(t\\) \u3092\u6b63\u898f\u76f4\u4ea4\u5316\u3057\u3066\u57fa\u5e95\u306b\u52a0\u3048\u308b) \u3053\u3068\u3067\u3088\u308a\u826f\u3044\u8fd1\u4f3c\u56fa\u6709\u5bfe\u3092\u5f97\u308b\u65b9\u6cd5\u3092\u30e4\u30b3\u30d3\u30fb\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u3068\u3044\u3046.<\/p>\n<p>\u4e0a\u5f0f\u3092 \\(Ax = \\lambda x\\) \u306b\u4ee3\u5165\u3059\u308b\u3068\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n(A &#8211; \\lambda I)t = -Au + \\lambda u<br \/>\n\\]\n\\(u\\) \u306e\u76f4\u4ea4\u88dc\u7a7a\u9593\u3078\u306e\u5c04\u5f71\u3092\u8868\u3059\u884c\u5217 \\(P = I &#8211; uu^T\\) \u3092\u8003\u3048, \u4e0a\u5f0f\u306e\u4e21\u8fba\u306b\u5de6\u304b\u3089\u639b\u3051\u308b.<br \/>\n\\[<br \/>\nP(A &#8211; \\lambda I)t = -PAu + \\lambda Pu<br \/>\n\\]\n\u3053\u3053\u3067, \\(Pt = t, Pu = 0, PAu = (I &#8211; uu^T)Au = Au &#8211; \\theta u = r\\) \u306e\u95a2\u4fc2\u3088\u308a\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n(I &#8211; uu^T)(A &#8211; \\lambda I)(I &#8211; uu^T)t = -r<br \/>\n\\]\n\\(\\lambda\\) \u306f\u672a\u77e5\u6570\u306a\u306e\u3067 \\(\\theta\\) \u3067\u7f6e\u304d\u63db\u3048\u305f\u6b21\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u308a \\(t\\) \u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u3059\u308b (\u305f\u3060\u3057, \\(t^Hu = 0\\)). \u3053\u306e\u5f0f\u3092\u4fee\u6b63\u65b9\u7a0b\u5f0f\u3068\u3044\u3046.<br \/>\n\\[<br \/>\n(I &#8211; uu^T)(A &#8211; \\theta I)(I &#8211; uu^T)t = -r<br \/>\n\\]\n\\(t\\) \u306e\u8a08\u7b97\u306b\u306f\u7d76\u5bfe\u5024\u6700\u5927\u306e\u30ea\u30c3\u30c4\u5024\u3068\u30ea\u30c3\u30c4\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u308b. \u307e\u305f, \\(r\\) \u304c\u5341\u5206\u5c0f\u3055\u304f\u306a\u308c\u3070\u53ce\u675f\u3068\u307f\u306a\u3059.<\/p>\n<p>\u30e4\u30b3\u30d3\u30fb\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u3067\u306f\u4fee\u6b63\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u304c\u7a2e\u3005\u7814\u7a76\u3055\u308c\u3066\u3044\u308b. \u53b3\u5bc6\u306b\u89e3\u304f\u3068\u53ce\u675f\u304c\u901f\u3044\u304c, \u52b9\u7387\u3088\u304f\u8fd1\u4f3c\u7684\u306b\u89e3\u3044\u3066\u3082\u5b9f\u7528\u7684\u306a\u53ce\u675f\u304c\u5f97\u3089\u308c\u308b\u3068\u3055\u308c\u308b.<\/p>\n<p>\\(t\\) \u3092\u6c42\u3081\u308b\u306e\u306b\u6b21\u5f0f\u3092\u4f7f\u3046\u65b9\u6cd5\u3092\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u3068\u3044\u3044, \u30e4\u30b3\u30d3\u30fb\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u306e\u5143\u306b\u306a\u3063\u305f\u65b9\u6cd5\u3067\u3042\u308b.<br \/>\n\\[<br \/>\n(D_A &#8211; \\theta I)t = -r<br \/>\n\\]\n\u305f\u3060\u3057, \\(D_A\\) \u306f \\(A\\) \u306e\u5bfe\u89d2\u8981\u7d20\u304b\u3089\u306a\u308b\u5bfe\u89d2\u884c\u5217\u3067\u3042\u308b.<\/p>\n<p>\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u306f \\(t\\) \u3092\u6c42\u3081\u308b\u8a08\u7b97\u306f\u7c21\u5358\u3067\u3042\u308b\u304c, \u5bfe\u89d2\u8981\u7d20\u304c\u512a\u4f4d\u306a\u884c\u5217\u306e\u7d76\u5bfe\u5024\u306e\u5927\u304d\u3044\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u306e\u306b\u6709\u52b9\u3068\u3055\u308c\u308b.<\/p>\n<h3>5.5.3 \u5404\u89e3\u6cd5\u306e\u6bd4\u8f03: \u6570\u5024\u5b9f\u9a13 (1)<\/h3>\n<p>\u30c6\u30b9\u30c8\u7528\u306b, \u56fa\u6709\u5024 1, 2, &#8230;, N \u3092\u6301\u3064 N x N \u5bfe\u79f0\u30e9\u30f3\u30c0\u30e0\u884c\u5217\u3092\u751f\u6210\u3059\u308b. N = 100 \u3068\u3057, \u758e\u884c\u5217\u3068\u3059\u308b\u4ee3\u308f\u308a\u306b\u5e2f\u5e45 5 \u306e\u5e2f\u884c\u5217\u3068\u3059\u308b.<\/p>\n<p>\u521d\u671f\u6b8b\u5dee\u30d9\u30af\u30c8\u30eb\u3092 \\((1, 1, \\dots, 1)\\) \u3092\u6b63\u898f\u5316\u3057\u305f\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066, \u3079\u304d\u4e57\u6cd5, \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5, \u30e4\u30b3\u30d3\u30fb\u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5, \u30c7\u30d3\u30c3\u30c8\u30bd\u30f3\u6cd5\u3092\u7528\u3044\u3066\u89e3\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_1_exp1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6244\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_1_exp1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_1_exp1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u6a2a\u8ef8\u306f\u53cd\u5fa9\u56de\u6570 (= \u90e8\u5206\u7a7a\u9593\u306e\u6b21\u6570), \u7e26\u8ef8\u306f\u6700\u5927\u56fa\u6709\u5024\u3068\u305d\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u6b8b\u5dee\u30ce\u30eb\u30e0 \\(\\|r\\|\\) (\u305f\u3060\u3057, \\(r = Ax &#8211; \\lambda x\\)) \u3067\u3042\u308b. \u3069\u306e\u65b9\u6cd5\u3082 1 \u56de\u306e\u53cd\u5fa9\u3042\u305f\u308a 1 \u56de\u306e \\(Ax\\) \u306e\u4e57\u7b97\u304c\u5fc5\u8981\u3067\u3042\u308b. \u3079\u304d\u4e57\u6cd5\u4ee5\u5916\u3067\u306f\u305d\u306e\u4ed6\u306b\u90e8\u5206\u7a7a\u9593\u306e\u751f\u6210\u3084\u90e8\u5206\u7a7a\u9593\u306e\u56fa\u6709\u5024\u8a08\u7b97\u3082\u5fc5\u8981\u306a\u306e\u3067\u6b63\u3057\u3044\u6bd4\u8f03\u3068\u306f\u3044\u3048\u306a\u3044\u304c, \u5143\u306e\u7a7a\u9593\u306b\u6bd4\u3079\u3066\u90e8\u5206\u7a7a\u9593\u304c\u5c0f\u3055\u3051\u308c\u3070 \\(Ax\\) \u306e\u4e57\u7b97\u306b\u6700\u3082\u6642\u9593\u304c\u304b\u304b\u308b\u306e\u3067, \u50be\u5411\u3092\u8868\u3057\u3066\u3044\u308b\u3068\u3044\u3048\u308b.<\/p>\n<p>\u3053\u306e\u4f8b\u984c\u306e\u5834\u5408, \u3079\u304d\u4e57\u6cd5\u306f\u3044\u304b\u306b\u3082\u53ce\u675f\u304c\u9045\u304f, \u5c04\u5f71\u6cd5\u306e 3 \u3064\u306e\u6027\u80fd\u306e\u826f\u3055\u304c\u308f\u304b\u308b.<\/p>\n<h3>5.5.4 \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306e\u53ce\u675f<\/h3>\n<p>\u6b21\u306b\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306e\u53ce\u675f\u306e\u69d8\u5b50\u3092\u8abf\u3079\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (2)<\/h4>\n<p>\u4e0b\u56f3\u306f, \u4e0a\u306e\u4f8b\u984c\u306b\u304a\u3044\u3066\u53cd\u5fa9\u56de\u6570 k = 60, 80, 100, 120, 140 \u306e\u3068\u304d\u306e\u6c42\u3081\u3089\u308c\u305f\u56fa\u6709\u5024\u3059\u3079\u3066\u306b\u3064\u3044\u3066\u306e\u6b8b\u5dee\u30ce\u30eb\u30e0 \\(\\|r\\|\\) \u3092\u30d7\u30ed\u30c3\u30c8\u3057\u305f\u3082\u306e\u3067\u3042\u308b. \u6a2a\u8ef8\u306f\u6c42\u3081\u3089\u308c\u305f\u56fa\u6709\u5024\u306e\u5024 (\u6b63\u89e3\u306f 1, 2, &#8230;, 100) \u3067\u3042\u308b. \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306f\u4e21\u7aef\u306b\u8fd1\u3044\u56fa\u6709\u5024\u304b\u3089\u53ce\u675f\u3059\u308b\u50be\u5411\u304c\u3042\u308b\u3068\u3044\u308f\u308c\u3066\u3044\u308b\u304c, \u3053\u306e\u4f8b\u3067\u306f\u305d\u306e\u3068\u304a\u308a\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_2_exp2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6245\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_2_exp2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_2_exp2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (3)<\/h4>\n<p>\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306f\u521d\u671f\u6b8b\u5dee\u30d9\u30af\u30c8\u30eb\u306e\u9078\u3073\u65b9\u306b\u3088\u3063\u3066\u53ce\u675f\u306e\u69d8\u5b50\u304c\u5168\u304f\u7570\u306a\u308b. \u4f8b\u3048\u3070, \u4e0a\u306e\u4f8b\u3067\u521d\u671f\u6b8b\u5dee\u30d9\u30af\u30c8\u30eb\u3092 (1, 0, &#8230;, 0) \u306b\u5909\u3048\u3066\u307f\u308b\u3068, \u4e0b\u306e\u3088\u3046\u306b\u5927\u304d\u3044\u65b9\u306e\u56fa\u6709\u5024\u306e\u53ce\u675f\u304c\u9045\u304f\u306a\u3063\u305f. \u305f\u3060\u3057, k = 120 \u306b\u6ce8\u76ee\u3059\u308b\u3068\u5168\u4f53\u7684\u306b\u306f\u3080\u3057\u308d\u901f\u304f\u53ce\u675f\u3057\u3066\u3044\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_3_exp3.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6246\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_3_exp3.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_3_exp3-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h3>5.5.5 \u518d\u76f4\u4ea4\u5316<\/h3>\n<p>\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306f\u4e09\u9805\u6f38\u5316\u5f0f\u3067\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u304c\u7279\u9577\u3067\u3042\u308b\u304c, \u9006\u306b\u4e38\u3081\u8aa4\u5dee\u306e\u5f71\u97ff\u3092\u53d7\u3051\u3084\u3059\u3044\u3068\u3044\u3046\u5f31\u70b9\u304c\u3042\u308b. \u3059\u306a\u308f\u3061, 2 \u3064\u3088\u308a\u4ee5\u524d\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3092\u53c2\u7167\u3057\u306a\u3044\u306e\u3067\u8a08\u7b97\u3092\u9032\u3081\u308b\u305f\u3081\u306b\u4e38\u3081\u8aa4\u5dee\u306e\u5f71\u97ff\u306b\u3088\u308a\u4e00\u6b21\u5f93\u5c5e\u306b\u306a\u308a\u3084\u3059\u3044. \u305d\u306e\u305f\u3081, \u53ce\u675f\u304c\u9045\u304f\u306a\u3063\u305f\u308a, \u507d\u306e\u56fa\u6709\u5024\u304c\u73fe\u308c\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3042\u308b.<\/p>\n<p>\u3053\u306e\u5bfe\u7b56\u3068\u3057\u3066\u306f, \u5f97\u3089\u308c\u3066\u3044\u308b\u3059\u3079\u3066\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3068\u6bce\u56de\u76f4\u4ea4\u5316\u3057\u76f4\u3059\u65b9\u6cd5 (\u518d\u76f4\u4ea4\u5316\u3068\u3044\u3046) \u3084, \u3042\u308b\u57fa\u6e96\u3092\u8a2d\u3051\u3066\u5fc5\u8981\u3068\u307f\u306a\u3055\u308c\u305f\u6642\u3060\u3051\u518d\u76f4\u4ea4\u5316\u3059\u308b\u65b9\u6cd5\u306a\u3069\u304c\u8003\u3048\u3089\u308c\u3066\u3044\u308b. \u305f\u3060\u3057, \u518d\u76f4\u4ea4\u5316\u306e\u305f\u3081\u306b\u306f\u3059\u3079\u3066\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3092\u4fdd\u5b58\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a, \u8a08\u7b97\u91cf\u3082\u5927\u304d\u3044\u3068\u3044\u3046\u8ab2\u984c\u304c\u3042\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (4)<\/h4>\n<p>\u6570\u5024\u5b9f\u9a13 (2) \u306b\u304a\u3044\u3066, \u6bce\u56de\u518d\u76f4\u4ea4\u5316\u3092\u884c\u3046\u3088\u3046\u306b\u5909\u66f4\u3059\u308b\u3068\u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_4_exp4.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6247\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_4_exp4.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_4_exp4-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>k = 120 \u4ee5\u4e0a\u3067\u660e\u3089\u304b\u306b\u7cbe\u5ea6\u304c\u826f\u304f\u306a\u3063\u3066\u3044\u308b (\u53ce\u675f\u304c\u901f\u304f\u306a\u3063\u3066\u3044\u308b) \u306e\u304c\u308f\u304b\u308b. \u307e\u305f, \u507d\u306e\u56fa\u6709\u5024 (\u4ed6\u306b\u6bd4\u3079\u3066\u660e\u3089\u304b\u306b\u7cbe\u5ea6\u306e\u60aa\u3044\u70b9) \u304c\u306a\u304f\u306a\u3063\u3066, \u4e00\u6b21\u5f93\u5c5e\u306b\u306a\u3063\u305f\u5f8c\u306f\u4f59\u5206\u306a\u56fa\u6709\u5024\u306e\u5024\u306f 0 \u306b\u306a\u3063\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b.<\/p>\n<h3>5.5.6 \u91cd\u8907\u56fa\u6709\u5024<\/h3>\n<p>\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3067\u306f\u91cd\u8907\u56fa\u6709\u5024\u304c\u3042\u308b\u5834\u5408\u306b\u306f (\u4e38\u3081\u8aa4\u5dee\u304c\u306a\u3051\u308c\u3070) 1 \u500b\u3057\u304b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044. \u305f\u3060\u3057, \u5b9f\u969b\u306b\u306f\u8aa4\u5dee\u306e\u305f\u3081\u306b\u5225\u3005\u306e\u56fa\u6709\u5024\u3068\u307f\u306a\u3057\u3066\u6c42\u3081\u3089\u308c\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3042\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (5)<\/h4>\n<p>\u4ee5\u4e0b\u306e\u5b9f\u9a13\u306f\u4e0a\u306e\u4f8b\u984c\u305d\u306e\u307e\u307e\u3067\u306f\u898b\u306b\u304f\u304f\u306a\u308b\u306e\u3067, N = 20, \u5e2f\u5e45 2 \u3068\u5c0f\u578b\u5316\u3057\u3066\u56fa\u6709\u5024 1, 2, &#8230;, 20 \u3092\u6301\u3064 20 x 20 \u5bfe\u79f0\u30e9\u30f3\u30c0\u30e0\u884c\u5217\u3092\u751f\u6210\u3059\u308b. \u3053\u308c\u306b\u521d\u671f\u6b8b\u5dee\u30d9\u30af\u30c8\u30eb\u3092 (1, 0, &#8230;, 0) \u3068\u3057\u3066\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3092\u9069\u7528\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_5_exp5_1.png\" alt=\"\" width=\"793\" height=\"415\" class=\"aligncenter size-full wp-image-6248\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_5_exp5_1.png 793w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_5_exp5_1-300x157.png 300w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_5_exp5_1-768x402.png 768w\" sizes=\"auto, (max-width: 793px) 100vw, 793px\" \/><\/p>\n<p>k = 16, 18, &#8230;, 24 \u306f\u53cd\u5fa9\u56de\u6570\u3067, \u305d\u308c\u305e\u308c\u306e\u5de6\u306e\u5217\u304c\u6c42\u3081\u3089\u308c\u305f\u56fa\u6709\u5024, \u53f3\u306e\u5217\u304c\u305d\u306e\u6b8b\u5dee\u30ce\u30eb\u30e0 ||r|| \u3067\u3042\u308b. \u3053\u306e\u5834\u5408, k = 20 \u3067\u5168\u56fa\u6709\u5024\u304c\u304d\u308c\u3044\u306b\u6c42\u3081\u3089\u308c\u3066\u3044\u308b. \u3053\u308c\u3092, \u6a2a\u8ef8 = \u56fa\u6709\u5024, \u7e26\u8ef8 = \u6b8b\u5dee\u30ce\u30eb\u30e0\u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_6_exp5_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6249\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_6_exp5_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_6_exp5_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u6b21\u306b, \u30c6\u30b9\u30c8\u884c\u5217\u306e\u56fa\u6709\u5024\u304c 1, 1, 3, 4, 5, 6, 6, 7, 8, 9, &#8230;, 20 (5 \u3064\u3054\u3068\u306b\u91cd\u8907\u56fa\u6709\u5024) \u3068\u306a\u308b\u3088\u3046\u306b\u5909\u3048\u3066\u540c\u69d8\u306b\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_7_exp5_3.png\" alt=\"\" width=\"793\" height=\"415\" class=\"aligncenter size-full wp-image-6250\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_7_exp5_3.png 793w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_7_exp5_3-300x157.png 300w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_7_exp5_3-768x402.png 768w\" sizes=\"auto, (max-width: 793px) 100vw, 793px\" \/><\/p>\n<p>\u30d7\u30ed\u30c3\u30c8\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_8_exp5_4.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6239\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_8_exp5_4.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_8_exp5_4-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u91cd\u8907\u56fa\u6709\u5024\u306e\u305f\u3081\u306b\u3059\u3063\u304d\u308a\u3068\u306f\u53ce\u675f\u3057\u306a\u304f\u306a\u3063\u305f\u306e\u304c\u308f\u304b\u308b.<\/p>\n<h3>5.5.7 \u30d6\u30ed\u30c3\u30af\u30fb\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5<\/h3>\n<p>p x p \u5c0f\u884c\u5217\u3092\u3072\u3068\u3064\u306e\u8981\u7d20\u3068\u307f\u306a\u3057\u3066, \u305d\u308c\u306b\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306e\u624b\u9806\u3092\u9069\u7528\u3059\u308b\u65b9\u6cd5\u3092\u30d6\u30ed\u30c3\u30af\u30fb\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3068\u3044\u3046. \u3053\u308c\u3092\u7528\u3044\u308b\u3068\u91cd\u8907\u5ea6 p \u307e\u3067\u306e\u91cd\u8907\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>\\(r\\) \u3084 \\(v\\) \u306a\u3069\u306e\u30d9\u30af\u30c8\u30eb\u306f n x p \u884c\u5217 (p \u672c\u306e\u30d9\u30af\u30c8\u30eb) \u3068\u306a\u308b. \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3067\u5f97\u3089\u308c\u308b\u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u306f\u6b21\u306e\u3088\u3046\u306b kp x kp \u30d6\u30ed\u30c3\u30af\u4e09\u91cd\u5bfe\u89d2\u884c\u5217\u306b\u306a\u308b.<br \/>\n\\[<br \/>\nT_k =<br \/>\n\\begin{pmatrix}<br \/>\n\\alpha_1 &amp; \\beta_2^T \\\\<br \/>\n\\beta_2 &amp; \\alpha_2 &amp; \\beta_3^T &amp; &amp; &amp; 0 \\\\<br \/>\n&amp; \\beta_3 &amp; \\alpha_3 &amp; \\beta_4^T \\\\<br \/>\n&amp; &amp; &amp; \\ddots \\\\<br \/>\n0 &amp; &amp; &amp; \\beta_{k-1} &amp; \\alpha_{k-1} &amp; \\beta_k^T \\\\<br \/>\n&amp; &amp; &amp; &amp; \\beta_k &amp; \\alpha_k \\\\<br \/>\n\\end{pmatrix}<br \/>\n\\]\n\u305f\u3060\u3057, \\(\\alpha_i\\) \u306f p x p \u5bfe\u79f0\u884c\u5217, \\(\\beta_i\\) \u306f p x p \u4e0a\u4e09\u89d2\u884c\u5217\u3067\u3042\u308b.<\/p>\n<p>\u4ee5\u4e0b, \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3068\u540c\u69d8\u306b kp x kp \u884c\u5217 \\(T_k\\) \u306e\u56fa\u6709\u5024 (\u30ea\u30c3\u30c4\u5024) \u3092 \\(\\theta\\), \u56fa\u6709\u30d9\u30af\u30c8\u30eb (\u30ea\u30c3\u30c4\u30d9\u30af\u30c8\u30eb) \u3092 \\(y\\) \u3068\u3059\u308b. \\(T_k\\) \u306e\u56fa\u6709\u5024\u306f\u5bfe\u79f0\u5e2f\u884c\u5217\u306e\u56fa\u6709\u5024\u554f\u984c\u3068\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<br \/>\n\\[<br \/>\nT_ky = \\theta y<br \/>\n\\]\n<h4>\u6570\u5024\u5b9f\u9a13 (6)<\/h4>\n<p>\u6570\u5024\u5b9f\u9a13 (5) \u306e\u91cd\u8907\u56fa\u6709\u5024\u306e\u4f8b\u984c\u306b p = 2 \u3068\u3057\u3066\u30d6\u30ed\u30c3\u30af\u30fb\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3092\u9069\u7528\u3059\u308b. \u521d\u671f\u6b8b\u5dee\u30d9\u30af\u30c8\u30eb\u306f (1, 0, &#8230;, 0) \u304a\u3088\u3073 (0, 1, &#8230;, 0) \u3068\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_9_exp6_1.png\" alt=\"\" width=\"793\" height=\"415\" class=\"aligncenter size-full wp-image-6240\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_9_exp6_1.png 793w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_9_exp6_1-300x157.png 300w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_9_exp6_1-768x402.png 768w\" sizes=\"auto, (max-width: 793px) 100vw, 793px\" \/><\/p>\n<p>k = 20 \u3067\u91cd\u8907\u56fa\u6709\u5024\u3092\u542b\u3081\u305f\u5168\u56fa\u6709\u5024\u304c\u304d\u308c\u3044\u306b\u6c42\u3081\u3089\u308c\u305f. \u30d7\u30ed\u30c3\u30c8\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_10_exp6_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6241\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_10_exp6_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_10_exp6_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h3>5.5.8 \u30ea\u30b9\u30bf\u30fc\u30c8<\/h3>\n<p>\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5, \u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u306a\u3069\u306e\u5c04\u5f71\u6cd5\u306e\u76ee\u7684\u306f, \u5927\u304d\u3044 n \u306e n x n \u884c\u5217\u306e\u6570\u500b\u306e\u56fa\u6709\u5024\u3092\u5c11\u306a\u3044\u53cd\u5fa9\u56de\u6570 (= k &lt;&lt; n) \u3067\u6c42\u3081\u308b\u3053\u3068\u3067\u3042\u3063\u305f.<\/p>\n<p>\u5927\u304d\u306a n \u306e\u884c\u5217\u306b\u5bfe\u3059\u308b\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3084\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u3092\u5358\u7d14\u306b\u53ce\u675f\u3059\u308b\u307e\u3067\u53cd\u5fa9\u3059\u308b\u3068, \u90e8\u5206\u7a7a\u9593\u306e\u6b21\u5143\u6570 k \u304c\u3069\u3093\u3069\u3093\u5927\u304d\u304f\u306a\u308a, \u5fc5\u8981\u30e1\u30e2\u30ea\u30fc\u91cf\u3082\u5897\u5927\u3057, \u90e8\u5206\u7a7a\u9593\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u81ea\u4f53\u304c\u56f0\u96e3\u306b\u306a\u3063\u3066\u306f\u56f0\u308b. \u305d\u3053\u3067, k \u306e\u4e0a\u9650\u3092\u5b9a\u3081 (m \u3068\u8868\u3059), \u4e0a\u9650\u306b\u9054\u3057\u305f\u3089\u30ea\u30b9\u30bf\u30fc\u30c8\u3059\u308b\u65b9\u6cd5\u304c\u8003\u3048\u3089\u308c\u308b. \u3053\u308c\u306b\u3088\u308a\u5fc5\u8981\u30e1\u30e2\u30ea\u30fc\u91cf\u306e\u4e0a\u9650\u3092\u3042\u3089\u304b\u3058\u3081\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3057, \u90e8\u5206\u7a7a\u9593\u304c\u5fc5\u8981\u4ee5\u4e0a\u306b\u5927\u304d\u304f\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u3067\u304d\u308b.<\/p>\n<p>\u30ea\u30b9\u30bf\u30fc\u30c8\u6642\u306b\u306f\u3059\u3067\u306b\u6c42\u3081\u305f m \u672c\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3092\u6368\u3066\u3066, \u65b0\u305f\u306a\u521d\u671f\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3092\u3084\u308a\u76f4\u3059\u304c, \u3053\u306e\u30d9\u30af\u30c8\u30eb\u3092\u3046\u307e\u304f\u9078\u3070\u306a\u3044\u3068\u53ce\u675f\u3057\u306a\u3044. \u3059\u3067\u306b\u6c42\u3081\u305f m \u672c\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u304b\u3089\u5f97\u3089\u308c\u308b\u60c5\u5831\u3092\u4f7f\u3063\u3066, \u6c42\u3081\u3088\u3046\u3068\u3059\u308b\u56fa\u6709\u5024\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u6210\u5206\u3092\u306a\u308b\u3079\u304f\u591a\u304f\u542b\u3093\u3067\u3044\u308b\u3082\u306e\u3092\u9078\u3070\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044. \u305d\u306e\u305f\u3081\u306b\u306f, \u30c1\u30a7\u30d3\u30b7\u30a7\u30d5\u591a\u9805\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3082\u306e\u306a\u3069\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u308b.<\/p>\n<p>\u30ea\u30b9\u30bf\u30fc\u30c8\u6642\u306e\u65b0\u305f\u306a\u521d\u671f\u30d9\u30af\u30c8\u30eb\u3092\u8907\u6570\u672c\u3068\u3059\u308b\u65b9\u6cd5\u3082\u3042\u308b. \u305d\u306e\u4f8b\u3068\u3057\u3066 Implicit restarting \u3068\u3088\u3070\u308c\u308b\u65b9\u6cd5\u3092\u4ee5\u4e0b\u306b\u8aac\u660e\u3059\u308b.<\/p>\n<h4>5.5.8.1 Implicit restarting<\/h4>\n<p>k \u500b\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u305f\u3044\u3082\u306e\u3068\u3059\u308b. m (&gt; k) \u3092\u9078\u3073, \u53cd\u5fa9\u56de\u6570\u304c m \u306b\u9054\u3057\u305f\u3089\u30ea\u30b9\u30bf\u30fc\u30c8\u3059\u308b\u3082\u306e\u3068\u3059\u308b.<\/p>\n<p>\u624b\u9806\u3068\u3057\u3066\u306f, \u307e\u305a\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u6cd5\u3092 m \u56de\u53cd\u5fa9\u3059\u308b. \u6b21\u306b, \u6c42\u3081\u3088\u3046\u3068\u3059\u308b k \u500b\u306e\u56fa\u6709\u5024\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u6210\u5206\u3092\u306a\u308b\u3079\u304f\u591a\u304f\u542b\u3093\u3067\u3044\u308b k \u672c\u306e\u65b0\u305f\u306a\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u3092\u73fe\u5728\u306e m \u672c\u306e\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u304b\u3089\u518d\u69cb\u6210\u3057, k + 1 \u56de\u76ee\u306e\u53cd\u5fa9\u304b\u3089\u30ea\u30b9\u30bf\u30fc\u30c8\u3059\u308b. \u518d\u3073 m \u56de\u306b\u9054\u3057\u305f\u3089\u540c\u69d8\u306e\u624b\u9806\u3092\u7e70\u308a\u8fd4\u3059.<\/p>\n<p>m \u56de\u53cd\u5fa9\u5f8c\u306e\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u5206\u89e3\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b.<br \/>\n\\[<br \/>\nAV_m = V_m H_m + h_{m+1,m} v_{m+1} e_m^T<br \/>\n\\]\n\\(H_m\\) \u306b\u5bfe\u3057\u3066\u30b7\u30d5\u30c8\u4ed8\u304d QR \u6cd5\u3092 p (= m &#8211; k) \u56de\u53cd\u5fa9\u3057\u305f\u3082\u306e\u3092 \\(H_m^+\\) \u3068\u8868\u3059\u3068\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064.<br \/>\n\\[<br \/>\nAV_m^+ = V_m^+ H_m^+ + h_{m+1,m} v_{m+1} e_m^T<br \/>\n\\]\n\u305f\u3060\u3057, \\(V_m^+ = V_mQ, H_m^+ = Q^TH_mQ, Q = Q_1 Q_2 \\dots Q_p\\) \u3067\u3042\u308b.<\/p>\n<p>\u30b7\u30d5\u30c8\u4ed8\u304d QR \u6cd5\u306b\u4f7f\u7528\u3059\u308b\u30b7\u30d5\u30c8\u306e\u5024\u306e\u9078\u3073\u65b9\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u304c\u8003\u3048\u3089\u308c\u308b\u304c, \u4e00\u4f8b\u3068\u3057\u3066, \\(H_m\\) \u306e m \u500b\u306e\u56fa\u6709\u5024\u3092\u5fc5\u8981\u306a k \u500b\u3068\u4e0d\u8981\u306a p \u500b\u306b\u5206\u3051\u305f\u3068\u304d\u306b, \u30b7\u30d5\u30c8\u5024\u3092\u4e0d\u8981\u306a p \u500b\u306e\u56fa\u6709\u5024\u306b\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u306b\u3059\u308b. \u305d\u3046\u3059\u308b\u3068, \\(H_m^+\\) \u306e\u5de6\u4e0a\u90e8\u5206\u306e k x k \u884c\u5217\u306f\u5fc5\u8981\u306a k \u500b\u306e\u56fa\u6709\u5024\u3092\u6301\u3064\u3053\u3068\u306b\u306a\u308b\u306e\u3067, \u3053\u308c\u3068 \\(V_m^+\\) \u306e\u5de6\u4e0a\u90e8\u5206\u306e k x k \u884c\u5217\u3092 k \u56de\u53cd\u5fa9\u5f8c\u306e\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u5206\u89e3\u3068\u3057\u3066\u30ea\u30b9\u30bf\u30fc\u30c8\u3059\u308c\u3070\u3088\u3044.<\/p>\n<p>\u4ee5\u4e0a\u306e\u65b9\u6cd5\u3092 Implicitly restarted Arnordi method (IRAM) \u3068\u3044\u3046. \u540c\u69d8\u306e\u624b\u9806\u3092\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u306b\u9069\u7528\u3057\u305f\u3082\u306e\u306f Implicitly restarted Lanczos method (IRLM) \u3068\u3088\u3070\u308c\u308b. \u3053\u306e\u65b9\u6cd5\u3067\u306f\u30b7\u30d5\u30c8\u5024\u3092\u3046\u307e\u304f\u9078\u3076\u3053\u3068\u306b\u3088\u308a\u72d9\u3063\u305f\u56fa\u6709\u5024\u3092\u512a\u5148\u7684\u306b\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<h4>\u6570\u5024\u5b9f\u9a13 (7)<\/h4>\n<p>\u6570\u5024\u5b9f\u9a13 (1) \u3068\u540c\u3058\u30c6\u30b9\u30c8\u554f\u984c\u306b IRLM \u3092\u9069\u7528\u3059\u308b.<\/p>\n<p>\u30c6\u30b9\u30c8\u884c\u5217\u306f\u56fa\u6709\u5024 1, 2, &#8230;, N \u3092\u6301\u3064 N x N \u5bfe\u79f0\u30e9\u30f3\u30c0\u30e0\u884c\u5217\u3067\u3042\u308b. N = 100 \u3068\u3057, \u5e2f\u5e45 5 \u306e\u5e2f\u884c\u5217\u3068\u3059\u308b. \u521d\u671f\u6b8b\u5dee\u30d9\u30af\u30c8\u30eb\u3092 (1, 1, &#8230;, 1) \u3092\u6b63\u898f\u5316\u3057\u305f\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066, \u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3068 IRLM (k = 5, m = 10) \u3092\u7528\u3044\u3066\u89e3\u304f\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u3063\u305f. \u306a\u304a, IRLM \u3067\u306f\u5927\u304d\u3044 k \u500b\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3088\u3046\u306b\u30b7\u30d5\u30c8\u5024\u3092\u8a2d\u5b9a\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_11_exp7_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6242\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_11_exp7_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_11_exp7_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u6a2a\u8ef8\u306f\u30e9\u30f3\u30c1\u30e7\u30b9\u53cd\u5fa9\u56de\u6570, \u7e26\u8ef8\u306f\u6700\u5927\u56fa\u6709\u5024\u3068\u305d\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u306e\u6b8b\u5dee\u30ce\u30eb\u30e0 \\(\\|r\\|\\) (\u305f\u3060\u3057, \\(r = Ax &#8211; \\lambda x\\)) \u3067\u3042\u308b.<\/p>\n<p>\u672c\u6765\u306e\u30e9\u30f3\u30c1\u30e7\u30b9\u6cd5\u3088\u308a\u306f\u9045\u304f\u306a\u308b\u304c\u6bd4\u8f03\u7684\u826f\u597d\u306b\u53ce\u675f\u3057\u3066\u3044\u308b. \u306a\u304a, m \u3092\u5927\u304d\u304f\u3059\u308b\u3068\u53ce\u675f\u306f\u901f\u304f\u306a\u308b. \u6b21\u306b k = 5, m = 20 \u306e\u4f8b\u3092\u793a\u3059.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_11_exp7_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-6243\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_11_exp7_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_11_exp7_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h3>5.5.9 \u4e00\u822c\u5316\u56fa\u6709\u5024\u554f\u984c<\/h3>\n<p>\u4e00\u822c\u5316\u56fa\u6709\u5024\u554f\u984c\u306f\u6b21\u5f0f\u3067\u8868\u3055\u308c\u308b.<br \/>\n\\[<br \/>\nAx = \\lambda Bx<br \/>\n\\]\nA \u3068 B \u306f n x n \u884c\u5217\u3067, \u03bb \u3092\u4e00\u822c\u5316\u56fa\u6709\u5024, x \u3092\u305d\u306e\u4e00\u822c\u5316\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3046. \u30e2\u30c7\u30eb\u3092\u96e2\u6563\u5316\u3057\u305f\u5834\u5408\u306a\u3069\u306b\u4e0a\u5f0f\u306e\u3088\u3046\u306a\u5f62\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u56fa\u6709\u5024\u554f\u984c\u304c\u73fe\u308c\u308b\u3053\u3068\u304c\u3042\u308b. \u3053\u306e\u5834\u5408\u306e\u4e3b\u306a\u89e3\u6cd5\u3092\u4ee5\u4e0b\u306b\u793a\u3059.<\/p>\n<h4>5.5.9.1 \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5<\/h4>\n<p>B \u304c\u6b63\u5b9a\u5024\u5bfe\u79f0\u3067 \\(LL^T\\) \u3068\u30b3\u30ec\u30b9\u30ad\u30fc\u5206\u89e3\u3067\u304d\u308b\u5834\u5408, \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c<br \/>\n\\[<br \/>\n(L^{-1}AL^{-T})z = \\lambda z<br \/>\n\\]\n\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u308a\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>\u5143\u306e\u554f\u984c\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb x \u306f, \u53ce\u675f\u5f8c\u306b \\(L^Tx = z\\) \u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u308a\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>\u3053\u306e\u65b9\u6cd5\u306f,\u30d5\u30a3\u30eb\u30a4\u30f3\u306b\u3088\u308a\u4e0a\u306e\u5909\u63db\u304c\u96e3\u3057\u3044\u5834\u5408\u306a\u3069\u9069\u3055\u306a\u3044\u3053\u3068\u3082\u3042\u308b.<\/p>\n<h4>5.5.9.2 \u30b9\u30da\u30af\u30c8\u30eb\u5909\u63db\u306b\u3088\u308b\u65b9\u6cd5<\/h4>\n<p>\u30b7\u30d5\u30c8 \\(\\mu\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u304c\u6210\u308a\u7acb\u3064.<br \/>\n\\[<br \/>\nAx = \\lambda Bx &lt;=&gt; (A &#8211; \\mu B)x = (\\lambda &#8211; \\mu)Bx<br \/>\n\\]\n\u3053\u308c\u3088\u308a\u6b21\u306e\u3088\u3046\u306a\u5909\u63db\u304c\u6210\u308a\u7acb\u3061, \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c\u306b\u5909\u63db\u3067\u304d\u308b.<br \/>\n\\[<br \/>\n(A &#8211; \\mu B)^{-1}Bx = \\theta x, \\space \u305f\u3060\u3057 \\space \\theta = 1\/(\\lambda &#8211; \\mu)<br \/>\n\\]\n\u3053\u3053\u3067, \\(A\\) \u304c\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408, \u5185\u7a4d\u3092 \\(\\lt x, y \\gt = x^TBy\\) \u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306b\u3088\u308a\u30e9\u30f3\u30c1\u30e7\u30b9\uff0f\u30a2\u30fc\u30ce\u30eb\u30c7\u30a3\u904e\u7a0b\u306e\u5bfe\u79f0\u6027\u304c\u4fdd\u305f\u308c\u308b.<\/p>\n<p>\u3053\u306e\u65b9\u6cd5\u3067\u306f \\((A &#8211; \\mu B)^{-1}\\) \u3068\u30d9\u30af\u30c8\u30eb\u306e\u4e57\u7b97\u306e\u8a08\u7b97\u304c\u7e70\u308a\u8fd4\u3057\u5fc5\u8981\u306b\u306a\u308b.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>5.5.1 \u56fa\u6709\u5024\u554f\u984c\u306e\u6982\u8981 5.5.1.1 \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c n x n \u884c\u5217 \\(A\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u3092\u6e80\u305f\u3059 \\(\\lambda\\) \u3092\u56fa\u6709\u5024, \\(x\\) \u3092\u305d\u306e\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3068\u3044\u3046. \\[ Ax = \\lambda [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-6229","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"5.5.1 \u56fa\u6709\u5024\u554f\u984c\u306e\u6982\u8981 5.5.1.1 \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c n x n \u884c\u5217 \\(A\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u3092\u6e80\u305f\" \/>\n\t<meta name=\"robots\" content=\"max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n\t<meta name=\"author\" content=\"Administrator\"\/>\n\t<meta name=\"google-site-verification\" content=\"5PEQMQVhF0wv5i-xMYW9a3HzuBwixzVduoR2arr5UDM\" \/>\n\t<meta name=\"msvalidate.01\" content=\"EEB9704E04960338720AEA89E77E749F\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.1.1\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#article\",\"name\":\"5.5 \\u56fa\\u6709\\u5024\\u30fb\\u56fa\\u6709\\u30d9\\u30af\\u30c8\\u30eb | K \\u30c6\\u30af\\u30ce\\u30ed\\u30b8\\u30fc\",\"headline\":\"5.5 \\u56fa\\u6709\\u5024\\u30fb\\u56fa\\u6709\\u30d9\\u30af\\u30c8\\u30eb\",\"author\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/author\\\/wadmin\\\/#author\"},\"publisher\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/#organization\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2026\\\/09\\\/5-5_1_exp1.png\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#articleImage\",\"width\":640,\"height\":480},\"datePublished\":\"2026-09-12T22:05:22+09:00\",\"dateModified\":\"2026-09-12T22:05:22+09:00\",\"inLanguage\":\"ja\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#webpage\"},\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#webpage\"},\"articleSection\":\"XLPack \\u89e3\\u6cd5\\u7de8\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp#listItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.ktech.biz\\\/jp\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/category\\\/num\\\/#listItem\",\"name\":\"XLPack \\u89e3\\u6cd5\\u7de8\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/category\\\/num\\\/#listItem\",\"position\":2,\"name\":\"XLPack \\u89e3\\u6cd5\\u7de8\",\"item\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/category\\\/num\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#listItem\",\"name\":\"5.5 \\u56fa\\u6709\\u5024\\u30fb\\u56fa\\u6709\\u30d9\\u30af\\u30c8\\u30eb\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp#listItem\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#listItem\",\"position\":3,\"name\":\"5.5 \\u56fa\\u6709\\u5024\\u30fb\\u56fa\\u6709\\u30d9\\u30af\\u30c8\\u30eb\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/category\\\/num\\\/#listItem\",\"name\":\"XLPack \\u89e3\\u6cd5\\u7de8\"}}]},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/#organization\",\"name\":\"K \\u30c6\\u30af\\u30ce\\u30ed\\u30b8\\u30fc\",\"description\":\"Excel\\u3067\\u672c\\u683c\\u7684\\u306a\\u6570\\u5024\\u8a08\\u7b97\\u304c\\u3067\\u304d\\u308b\\uff01\",\"url\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/author\\\/wadmin\\\/#author\",\"url\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/author\\\/wadmin\\\/\",\"name\":\"Administrator\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#authorImage\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/ba306ded26254eaa30f5f7d0a9a3a1555a04b1f34069c8d4ebf8c40646da82c4?s=96&d=mm&r=g\",\"width\":96,\"height\":96,\"caption\":\"Administrator\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#webpage\",\"url\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/\",\"name\":\"5.5 \\u56fa\\u6709\\u5024\\u30fb\\u56fa\\u6709\\u30d9\\u30af\\u30c8\\u30eb | K \\u30c6\\u30af\\u30ce\\u30ed\\u30b8\\u30fc\",\"description\":\"5.5.1 \\u56fa\\u6709\\u5024\\u554f\\u984c\\u306e\\u6982\\u8981 5.5.1.1 \\u6a19\\u6e96\\u56fa\\u6709\\u5024\\u554f\\u984c n x n \\u884c\\u5217 \\\\(A\\\\) \\u306b\\u3064\\u3044\\u3066\\u6b21\\u5f0f\\u3092\\u6e80\\u305f\",\"inLanguage\":\"ja\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/#website\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/num\\\/5-5_sparse\\\/#breadcrumblist\"},\"author\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/author\\\/wadmin\\\/#author\"},\"creator\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/author\\\/wadmin\\\/#author\"},\"datePublished\":\"2026-09-12T22:05:22+09:00\",\"dateModified\":\"2026-09-12T22:05:22+09:00\"},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/#website\",\"url\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/\",\"name\":\"K \\u30c6\\u30af\\u30ce\\u30ed\\u30b8\\u30fc\",\"description\":\"Excel\\u3067\\u672c\\u683c\\u7684\\u306a\\u6570\\u5024\\u8a08\\u7b97\\u304c\\u3067\\u304d\\u308b\\uff01\",\"inLanguage\":\"ja\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.ktech.biz\\\/jp\\\/#organization\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb | K \u30c6\u30af\u30ce\u30ed\u30b8\u30fc","description":"5.5.1 \u56fa\u6709\u5024\u554f\u984c\u306e\u6982\u8981 5.5.1.1 \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c n x n \u884c\u5217 \\(A\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u3092\u6e80\u305f","canonical_url":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/","robots":"max-snippet:-1, max-image-preview:large, max-video-preview:-1","keywords":"","webmasterTools":{"google-site-verification":"5PEQMQVhF0wv5i-xMYW9a3HzuBwixzVduoR2arr5UDM","msvalidate.01":"EEB9704E04960338720AEA89E77E749F","miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#article","name":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb | K \u30c6\u30af\u30ce\u30ed\u30b8\u30fc","headline":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb","author":{"@id":"https:\/\/www.ktech.biz\/jp\/author\/wadmin\/#author"},"publisher":{"@id":"https:\/\/www.ktech.biz\/jp\/#organization"},"image":{"@type":"ImageObject","url":"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/09\/5-5_1_exp1.png","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#articleImage","width":640,"height":480},"datePublished":"2026-09-12T22:05:22+09:00","dateModified":"2026-09-12T22:05:22+09:00","inLanguage":"ja","mainEntityOfPage":{"@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#webpage"},"isPartOf":{"@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#webpage"},"articleSection":"XLPack \u89e3\u6cd5\u7de8"},{"@type":"BreadcrumbList","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp#listItem","position":1,"name":"Home","item":"https:\/\/www.ktech.biz\/jp","nextItem":{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp\/category\/num\/#listItem","name":"XLPack \u89e3\u6cd5\u7de8"}},{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp\/category\/num\/#listItem","position":2,"name":"XLPack \u89e3\u6cd5\u7de8","item":"https:\/\/www.ktech.biz\/jp\/category\/num\/","nextItem":{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#listItem","name":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb"},"previousItem":{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp#listItem","name":"Home"}},{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#listItem","position":3,"name":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb","previousItem":{"@type":"ListItem","@id":"https:\/\/www.ktech.biz\/jp\/category\/num\/#listItem","name":"XLPack \u89e3\u6cd5\u7de8"}}]},{"@type":"Organization","@id":"https:\/\/www.ktech.biz\/jp\/#organization","name":"K \u30c6\u30af\u30ce\u30ed\u30b8\u30fc","description":"Excel\u3067\u672c\u683c\u7684\u306a\u6570\u5024\u8a08\u7b97\u304c\u3067\u304d\u308b\uff01","url":"https:\/\/www.ktech.biz\/jp\/"},{"@type":"Person","@id":"https:\/\/www.ktech.biz\/jp\/author\/wadmin\/#author","url":"https:\/\/www.ktech.biz\/jp\/author\/wadmin\/","name":"Administrator","image":{"@type":"ImageObject","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#authorImage","url":"https:\/\/secure.gravatar.com\/avatar\/ba306ded26254eaa30f5f7d0a9a3a1555a04b1f34069c8d4ebf8c40646da82c4?s=96&d=mm&r=g","width":96,"height":96,"caption":"Administrator"}},{"@type":"WebPage","@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#webpage","url":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/","name":"5.5 \u56fa\u6709\u5024\u30fb\u56fa\u6709\u30d9\u30af\u30c8\u30eb | K \u30c6\u30af\u30ce\u30ed\u30b8\u30fc","description":"5.5.1 \u56fa\u6709\u5024\u554f\u984c\u306e\u6982\u8981 5.5.1.1 \u6a19\u6e96\u56fa\u6709\u5024\u554f\u984c n x n \u884c\u5217 \\(A\\) \u306b\u3064\u3044\u3066\u6b21\u5f0f\u3092\u6e80\u305f","inLanguage":"ja","isPartOf":{"@id":"https:\/\/www.ktech.biz\/jp\/#website"},"breadcrumb":{"@id":"https:\/\/www.ktech.biz\/jp\/num\/5-5_sparse\/#breadcrumblist"},"author":{"@id":"https:\/\/www.ktech.biz\/jp\/author\/wadmin\/#author"},"creator":{"@id":"https:\/\/www.ktech.biz\/jp\/author\/wadmin\/#author"},"datePublished":"2026-09-12T22:05:22+09:00","dateModified":"2026-09-12T22:05:22+09:00"},{"@type":"WebSite","@id":"https:\/\/www.ktech.biz\/jp\/#website","url":"https:\/\/www.ktech.biz\/jp\/","name":"K \u30c6\u30af\u30ce\u30ed\u30b8\u30fc","description":"Excel\u3067\u672c\u683c\u7684\u306a\u6570\u5024\u8a08\u7b97\u304c\u3067\u304d\u308b\uff01","inLanguage":"ja","publisher":{"@id":"https:\/\/www.ktech.biz\/jp\/#organization"}}]}},"aioseo_meta_data":{"post_id":"6229","title":null,"description":null,"keywords":null,"keyphrases":{"focus":{"keyphrase":"","score":0,"analysis":{"keyphraseInTitle":{"score":0,"maxScore":9,"error":1}}},"additional":[]},"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":"","og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"Article","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":"-1","robots_max_videopreview":"-1","robots_max_imagepreview":"large","priority":null,"frequency":"default","location":null,"local_seo":null,"breadcrumb_settings":null,"limit_modified_date":false,"ai":{"faqs":[],"keyPoints":[],"schemas":[],"titles":[],"descriptions":[],"socialPosts":{"email":{"subject":"","preview":"","content":""},"linkedin":[],"twitter":[],"facebook":[],"instagram":[]}},"created":"2026-09-11 08:08:02","updated":"2026-09-12 13:05:22","seo_analyzer_scan_date":null,"focus_keyword":null,"additional_keywords":null,"truseo_locale":null},"_links":{"self":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/6229","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/comments?post=6229"}],"version-history":[{"count":10,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/6229\/revisions"}],"predecessor-version":[{"id":6251,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/6229\/revisions\/6251"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=6229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=6229"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=6229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}