{"provider_url":"https://hatena.blog","title":"\u7dda\u5f62\u4ee3\u6570\u52c9\u5f37\uff1a\u884c\u5217\uff15\u5206\u89e3 QR\u5206\u89e3(1)","blog_title":"\u672c\u5f53\u306f\u6016\u3044HPC & AI","author_url":"https://blog.hatena.ne.jp/keisukefukuda/","published":"2025-02-25 05:27:31","width":"100%","author_name":"keisukefukuda","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Ffreak-da.hatenablog.com%2Fentry%2F2025%2F02%2F25%2F052731\" title=\"\u7dda\u5f62\u4ee3\u6570\u52c9\u5f37\uff1a\u884c\u5217\uff15\u5206\u89e3 QR\u5206\u89e3(1) - \u672c\u5f53\u306f\u6016\u3044HPC &amp; AI\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","categories":[],"type":"rich","height":"190","url":"https://freak-da.hatenablog.com/entry/2025/02/25/052731","version":"1.0","blog_url":"https://freak-da.hatenablog.com/","provider_name":"Hatena Blog","description":"\uff08\u4ee5\u4e0b\u306f\u81ea\u7fd2\u8cc7\u6599\u3067\u3059\u3002\uff09 \u30b9\u30c8\u30e9\u30f3\u30b0\u6559\u6388\u306e\u884c\u5217\uff15\u5206\u89e3\u3001\u3068\u308a\u3042\u3048\u305a\u6b21\u306fQR\u5206\u89e3\u3002 QR\u5206\u89e3\u3068\u306f QR\u5206\u89e3\u3068\u306f\u3001\u884c\u5217 $ A $ \u3092 $ A = QR $ \u306e\u3088\u3046\u306b\u884c\u5217 $Q$ \u3068 $R$ \u306b\u5206\u89e3\u3059\u308b\u64cd\u4f5c\u3002\u3053\u3053\u3067\u3001$Q$\u306f\u76f4\u4ea4\u884c\u5217\u3001$R$\u306f\u4e0a\u4e09\u89d2\u884c\u3067\u3042\u308b\u3002 \u5229\u7528\u4e8b\u4f8b\u3068\u3057\u3066\u306f\u3001\u5358\u7d14\u306a\u4f8b\u3068\u3057\u3066\u306f \u9023\u7acb\u65b9\u7a0b\u5f0f $$ Ax=b $$ \u3092\u76f4\u63a5\u89e3\u304f\u3088\u308a\u3082\u3001$Q^{T}$ \u3092\u5de6\u304b\u3089\u304b\u3051\u3066 $$ RAx = Q^{T} b $$ \u3068\u3059\u308b\u3068\u3001\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002 \u8a08\u7b97\u65b9\u6cd5 QR\u5206\u89e3\u3092\u5b9f\u73fe\u3059\u308b\u6570\u5024\u8a08\u7b97\u624b\u6cd5\u3068\u3057\u3066\u3001 \u30b0\u30e9\u30e0\u30b7\u30e5\u30df\u30c3\u30c8\u306e\u76f4\u4ea4\u5316\u3092\u5229\u7528 Householder\u5909\u63db\u3092\u5229\u7528\u3001\u307e\u305f\u306f\u305d\u306e\u4e9c\u7a2e \u305d\u306e\u4ed6 \u304c\u3042\u308b\u304c\u3001\u307e\u305a\u306f\u2026","image_url":null}