{"id":546,"date":"2012-08-02T11:34:27","date_gmt":"2012-08-02T03:34:27","guid":{"rendered":"http:\/\/140.121.146.12\/wordpress\/?p=546"},"modified":"2012-08-02T11:34:27","modified_gmt":"2012-08-02T03:34:27","slug":"2012%e6%9c%80%e6%96%b0%e7%a0%94%e7%a9%b6%e5%a0%b1%e5%b0%8e%e9%a1%a7%e8%80%81%e5%b8%ab%e7%a0%94%e7%a9%b6%e5%ae%a4","status":"publish","type":"post","link":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/?p=546","title":{"rendered":"2012\u6700\u65b0\u7814\u7a76\u5831\u5c0e(\u9867\u8001\u5e2b\u7814\u7a76\u5ba4)"},"content":{"rendered":"<p>\t\t\t\t<![CDATA[<strong>\u5229\u7528\u985e\u725b\u9813\u52d5\u529b\u5b78\u65b9\u6cd5\u6c42\u89e3\u975e\u7dda\u6027\u75c5\u614b\u7cfb\u7d71\u4e26\u61c9\u7528\u65bc\u908a\u754c\u503c\u554f\u984c<\/strong>\n\u672c\u6587\u57fa\u65bc\u7d14\u91cf\u5f62\u5f0f\u4e4b\u540c\u502b\u6cd5\u63d0\u51fa\u5ee3\u7fa9\u52d5\u529b\u5b78\u65b9\u6cd5\u4ee5\u6c42\u89e3\u975e\u7dda\u6027\u4ee3\u6578\u65b9\u7a0b\u554f\u984c\u4e4b\u65b0\u65b9\u6cd5\u3002\u70ba\u63a8\u5c0e\u51fa\u7d14\u91cf\u5f62\u5f0f\u4e4b\u540c\u502b\u6cd5\uff0c\u9996\u5148\u5c07\u5411\u91cf\u5e7e\u4f55\u4e2d\u4e4b\u5411\u91cf\u540c\u502b\u51fd\u6578\u53d6\u5176\u5411\u91cf\u9577\u5ea6\uff0c\u4e26\u900f\u904e\u5167\u7a4d\u4ee5\u53d6\u5e73\u65b9\u7bc4\u6578\uff0c\u4e4b\u5f8c\u85c9\u7531\u5f15\u5165\u865b\u64ec\u6642\u9593\u51fd\u6578\u5f8c\uff0c\u4fbf\u53ef\u63a8\u5c0e\u5f97\u5ee3\u7fa9\u52d5\u529b\u5b78\u65b9\u6cd5\u3002\u85c9\u7531\u5f15\u5165\u8f49\u63db\u77e9\u9663\u4e4b\u6982\u5ff5\uff0c\u672c\u6587\u6240\u63d0\u51fa\u5ee3\u7fa9\u52d5\u529b\u5b78\u65b9\u6cd5\u53ef\u8f49\u63db\u6210\u4e09\u7a2e\u4e0d\u540c\u4e4b\u65b9\u6cd5\u5206\u5225\u70ba\u52d5\u529b\u725b\u9813\u6cd5\u3001\u52d5\u529b\u7121Jacobian\u53cd\u77e9\u9663\u6cd5\u3001\u53ca\u6d41\u5f62\u6307\u6578\u6536\u6582\u6f14\u7b97\u6cd5\u7b49\u4e09\u500b\u65b9\u6cd5\u3002\u540c\u6642\u85c9\u7531\u5ee3\u7fa9\u52d5\u529b\u5b78\u65b9\u6cd5\uff0c\u4f7f\u7528\u7279\u5b9a\u6642\u9593\u51fd\u6578\uff0c\u543e\u4eba\u4ea6\u53ef\u63a8\u5c0e\u51fa\u50b3\u7d71\u725b\u9813\u6cd5\uff0c\u6b64\u5916\u672c\u6587\u5ee3\u7fa9\u52d5\u529b\u5b78\u65b9\u6cd5\u4ea6\u5177\u6709\u6975\u5927\u6f5b\u529b\u63a8\u5c0e\u5176\u5b83\u52d5\u529b\u5b78\u65b9\u6cd5\u3002\n\u672c\u7814\u7a76\u6240\u63d0\u51fa\u4e4b\u65b0\u65b9\u6cd5\u53ef\u6c42\u89e3\u5927\u578b\u53ca\u5404\u7a2e\u5de5\u7a0b\u554f\u984c\u6240\u884d\u751f\u51fa\u4e4b\u975e\u7dda\u6027\u75c5\u614b\u7cfb\u7d71\u4e26\u61c9\u7528\u65bc\u908a\u754c\u503c\u554f\u984c\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u672c\u7814\u7a76\u6240\u63d0\u51fa\u4e4b\u65b9\u6cd5\u65bc\u8a08\u7b97\u904e\u7a0b\u4e2d\u4e0d\u9700\u518d\u884c\u6c42\u89e3Jacobian\u77e9\u9663\u4e4b\u53cd\u77e9\u9663\uff0c\u56e0\u6b64\u5177\u8f03\u9ad8\u4e4b\u6578\u503c\u7a69\u5b9a\u6027\uff0c\u540c\u6642\u4ea6\u7bc0\u7701\u5927\u91cf\u6578\u503c\u904b\u7b97\u4e4b\u6642\u9593\u3002\u6578\u503c\u6848\u4f8b\u4e4b\u5206\u6790\u7d50\u679c\u986f\u793a\uff0c\u672c\u7814\u7a76\u6240\u63d0\u51fa\u4e4b\u65b0\u65b9\u6cd5\u5177\u9ad8\u6548\u7387\u4ee5\u6c42\u89e3\u975e\u7dda\u6027\u4e4b\u554f\u984c\uff0c\u540c\u6642\u4ea6\u53ef\u660e\u986f\u63d0\u5347\u5206\u6790\u7cbe\u5ea6\u8207\u6536\u6582\u6027\uff0c\u5c0d\u65bc\u75c5\u614b\u7cfb\u7d71\u4e4b\u554f\u984c\u8207\u75c5\u614b\u521d\u59cb\u503c\u4e4b\u554f\u984c\u4ea6\u5177\u6709\u76f8\u7576\u597d\u4e4b\u8655\u7406\u80fd\u529b\u3002\n<strong>\u95dc\u9375\u5b57<\/strong>\uff1a\u52d5\u529b\u5b78\u65b9\u6cd5\uff0c\u7d14\u91cf\u540c\u502b\u51fd\u6578\uff0c\u64ec\u6642\u9593\u7a4d\u5206\u51fd\u6578\uff0c\u725b\u9813\u6cd5\uff0c\u52d5\u529b\u7121Jacobian\u53cd\u77e9\u9663\u6cd5\uff0c\u6d41\u5f62\u6307\u6578\u6536\u6582\u6f14\u7b97\u6cd5\u3002\n\u4e0b\u8f09\u672c\u6587(Download paper) <a href=\"http:\/\/140.121.146.12\/wordpress\/wordpress\/wp-content\/uploads\/2012\/08\/2011_cmes.2011.076.083.pdf\">2011_cmes.2011.076.083<\/a>\nPaper No. : CMES201107181934 Dynamical Newton-Like Methods for Solving Ill-Conditioned Systems of Nonlinear Equations with Applications to Boundary Value Problems by Cheng-Yu Ku, Weichung Yeih, Chein-Shan Liu published in &#8220;CMES: Computer Modeling in Engineering &amp; Sciences&#8221;.\nTech Science Press grants you permission to post this soft-reprint on your web-site, as well as distribute it, in a reasonable way, solely for the purpose of academic\/research exchanges with your immediate colleagues in your research community.\n&nbsp;\n<strong>ABSTRACT<\/strong><strong>:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>In this paper, a general dynamical method based on the construction of a scalar homotopy function to transform a vector function of non-linear algebraic equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of a transformation matrix, the proposed general dynamical method can be transformed into several dynamical Newton-like methods including the Dynamical Newton Method (DNM), the Dynamical Jacobian-Inverse Free Method (DJIFM) and the Manifold-Based Exponentially Convergent Algorithm (MBECA). From the general dynamical method, we can also derive the conventionalNewton method using a certain fictitious time-like function. The formulation presented in this paper demonstrates a variety of flexibility with the use of different transformation matrices to create other possible dynamical methods for solving NAEs. These three dynamical Newton-like methods are then adopted for the solution of ill-conditioned systems of nonlinear equations and applied to boundary value problems. Results reveal that taking advantages of the general dynamical method the proposed three dynamical Newton-like methods can improve the convergence and increase the numerical stability for solving NAEs especially for the system of nonlinear problems involving ill-conditioned Jacobian or poor initial values which cause convergence problems.\n<strong>Keyword<\/strong><strong>s<\/strong><strong>:<\/strong> dynamical method, scalar homotopy function, fictitious time-like function,Newton\u2019s method, dynamical Jacobian-inverse free method, manifold-based exponentially convergent algorithm.]]>\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\t\t\t\t<![CDATA[]]>\t\t<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[3,9],"class_list":["post-546","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-00_home","tag-uncategorized"],"_links":{"self":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/546","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=546"}],"version-history":[{"count":0,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/546\/revisions"}],"wp:attachment":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}