{"id":3824,"date":"2005-03-15T03:13:00","date_gmt":"2005-03-14T18:13:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3824"},"modified":"2021-08-12T12:01:18","modified_gmt":"2021-08-12T03:01:18","slug":"%ed%95%b4%ec%84%9d%ed%95%99%ec%97%90%ec%84%9c","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2005\/03\/15\/%ed%95%b4%ec%84%9d%ed%95%99%ec%97%90%ec%84%9c\/","title":{"rendered":"\ud574\uc11d\ud559\uc5d0\uc11c"},"content":{"rendered":"

\ub2e4\ubcc0\uc218 \ud574\uc11d\ud559\uc5d0\uc11c \ud544\uc694\ud55c \uac1c\ub150\ub4e4\uc785\ub2c8\ub2e4. <\/p>\n

\n

\ubbf8\ubd84\uc758 \uac1c\ub150<\/h2>\n<\/div>\n
\n

\ud569\uc131\ud568\uc218\uc758 \ubbf8\ubd84\ubc95<\/h2>\n<\/div>\n
\n

IFT(Inverse Function Theorem)<\/h2>\n
\n<\/div>\n
\n

\ub274\ud2bc\uc758 \uadfc\uc758 \uadfc\uc0ac\ubc95<\/h3>\n
\n

$ E,F$ \uac00 Banach \uacf5\uac04\uc774\uace0 $ f$ \ub294 $ x_0∈ E$ \uc758 \uadfc\ubc29 $ V$ \uc704\uc5d0\uc11c $ F$ \ub85c \uc815\uc758\ub41c \uc5f0\uc18d\ubbf8\ubd84\uac00\ub2a5\ud568\uc218\uc774\ub2e4. \ub2e4\uc74c\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \ub450 \uc2e4\uc218 $ β>0$ \uc640 $ λ>0$ \uac00 \uc874\uc7ac\ud55c\ub2e4\uace0 \ud558\uc790: <\/p>\n

    \n
  1. $ \\| f(x_0) \\| < β\/(2λ) $<\/li>\n
  2. \uad6c $ U: \\|x-x_0\\| < β$ \uc758 \ub0b4\ubd80\uc5d0\uc11c $ f’$ \uc758 oscillation\uc774 $ ≤1\/(2λ)$ \uc774\ub2e4.<\/li>\n
  3. \uac01 $ x∈ U$ \uc5d0 \ub300\ud558\uc5ec $ f'(x)$ \ub294 $ E$ \uc5d0\uc11c $ F$ \ub85c\uc758 isomorphism\uc774\uace0 $ \\|(f'(x))^{-1}\\|≤ λ$ \uc774\ub2e4.<\/li>\n<\/ol>\n

    \uc774\uc81c $ (z_n)$ \uc774 $ U$ \uc758 \uc784\uc758\uc758 sequence\ub77c\uace0 \ud558\uc790. \uc774 \ub54c, \\[ x_{n+1} = x_n – (f'(z_n))^{-1}\\cdot f(x_n)\\] \uc73c\ub85c \uc815\uc758\ub418\ub294 $ U$ \uc758 sequence $ (x_n)$ \uc774 \uc874\uc7ac\ud558\uc5ec, \uc774 sequence\ub294 $ U$ \uc758 \uc810 $ y$ \ub85c \uc218\ub834\ud558\uba70 $ y$ \ub294 $ U$ \uc5d0\uc11c \ubc29\uc815\uc2dd $ f(x)=0$ \uc758 \uc720\uc77c\ud55c \ud574\uc784\uc744 \ubcf4\uc5ec\ub77c. <\/p>\n

    ”’Hint”’: \uc2dd \\[ \\| f(b)-f(a)-f'(x_0)\\cdot(b-a) \\leq \\| b-a\\| \\cdot \\sup_{x\\in U} \\|f'(x)-f'(x_0)\\| \\] \ub97c \uc368\uc11c $ \\|x_n-x_{n-1}\\| < 2^{-n}β$ , $ \\|f(x_n)\\| < β\/(2^{n+1}λ)$ \uc784\uc744 \ubcf4\uc5ec\ub77c. <\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    \ub2e4\ubcc0\uc218 \ud574\uc11d\ud559\uc5d0\uc11c \ud544\uc694\ud55c \uac1c\ub150\ub4e4\uc785\ub2c8\ub2e4. \ubbf8\ubd84\uc758 \uac1c\ub150 \ud569\uc131\ud568\uc218\uc758 \ubbf8\ubd84\ubc95 IFT(Inverse Function Theorem) \ub274\ud2bc\uc758 \uadfc\uc758 \uadfc\uc0ac\ubc95 $ E,F$ \uac00 Banach \uacf5\uac04\uc774\uace0 $ f$ \ub294 $ x_0∈ E$ \uc758 \uadfc\ubc29 $ V$ \uc704\uc5d0\uc11c $ F$ \ub85c \uc815\uc758\ub41c \uc5f0\uc18d\ubbf8\ubd84\uac00\ub2a5\ud568\uc218\uc774\ub2e4. \ub2e4\uc74c\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \ub450 \uc2e4\uc218 $ β>0$ \uc640 $ λ>0$ \uac00 \uc874\uc7ac\ud55c\ub2e4\uace0 \ud558\uc790: $ \\| f(x_0) \\| < β\/(2λ) $ \uad6c … \ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3824","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"\uae40\uc601\uc6b1","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/ywkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3824","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/comments?post=3824"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3824\/revisions"}],"predecessor-version":[{"id":3825,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3824\/revisions\/3825"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3824"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3824"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}