{"provider_url":"https://hatena.blog","width":"100%","type":"rich","title":"Markov \u5144\u5f1f\u306e\u4e0d\u7b49\u5f0f","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Fall-for-nothing.com%2Fentry%2F2020%2F11%2F23%2F205352\" title=\"Markov \u5144\u5f1f\u306e\u4e0d\u7b49\u5f0f - \u7a7a\u8ad6\u4e0a\u306e\u7802\u3001\u697c\u95a3\u4e0a\u306e\u673a\u3002\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","categories":["\u6570\u5b66"],"published":"2020-11-23 20:53:52","description":"\u5b9a\u74061. (Markov \u5144\u5f1f\u306e\u4e0d\u7b49\u5f0f) $\\lVert f\\rVert\\coloneqq\\displaystyle\\max_{-1\\leqq x\\leqq1}|f(x)|$ \u3068\u5b9a\u3081, $p$ \u3092 $n$ \u6b21\u4ee5\u4e0b\u306e\u591a\u9805\u5f0f, $T_n(x)$ \u3092\u7b2c\u4e00\u7a2e Chebyshev \u591a\u9805\u5f0f\u3068\u3059\u308b\u3068, $$\\lVert p^{(k)}\\rVert\\leqq\\lVert T_n^{(k)}\\rVert\\lVert p\\rVert$$ \u304c\u6210\u308a\u7acb\u3061, \u7b49\u53f7\u6210\u7acb\u6761\u4ef6\u306f $p=\\pm T_n$ \u3067\u3042\u308b. \u8a3c\u660e. Shadrin (2005) \u3092\u53c2\u7167. $k=1$, $n=2$ \u3068\u3059\u308b\u3068 $\\lVert p'\\rVer\u2026","version":"1.0","blog_title":"\u7a7a\u8ad6\u4e0a\u306e\u7802\u3001\u697c\u95a3\u4e0a\u306e\u673a\u3002","url":"https://all-for-nothing.com/entry/2020/11/23/205352","image_url":null,"author_name":"all_for_nothing","height":"190","provider_name":"Hatena Blog","blog_url":"https://all-for-nothing.com/","author_url":"https://blog.hatena.ne.jp/all_for_nothing/"}