{"id":511,"date":"2018-08-08T09:12:13","date_gmt":"2018-08-08T12:12:13","guid":{"rendered":"http:\/\/blog.ufes.br\/isaacsantos\/?page_id=511"},"modified":"2020-03-03T22:17:41","modified_gmt":"2020-03-04T01:17:41","slug":"algebra-linear-numerica-2018-2","status":"publish","type":"page","link":"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/algebra-linear-numerica-2018-2\/","title":{"rendered":"\u00c1lgebra Linear Num\u00e9rica &#8211; 2019\/2"},"content":{"rendered":"<h1><span style=\"color: #ff0000\"><strong>Objetivo da disciplina<\/strong>:<\/span><\/h1>\n<ul>\n<li><span style=\"color: #000000\">Fornecer ao estudante as ferramentas b\u00e1sicas da \u00e1lgebra linear (num\u00e9rica) para constru\u00e7\u00e3o de algoritmos e m\u00e9todos num\u00e9ricos eficientes.<br \/>\n<\/span><\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\"><strong>Cursos<\/strong>:<\/span><\/h1>\n<ul>\n<li><span style=\"color: #000000\">Matem\u00e1tica Industrial<\/span><\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\"><strong>Hor\u00e1rio das aulas<\/strong>:<\/span><\/h1>\n<ul>\n<li><span style=\"color: #000000\">segundas 10:40 &#8211; 12:20 (Sala 11 &#8211; Eixo 1) e quartas 10:40 &#8211; 12:20 (Sala 01 &#8211; Eixo 1)<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #ff0000\"><strong>Programa da disciplina<\/strong>:<\/span><\/h2>\n<ol>\n<li><span style=\"color: #000000\"><strong>Fundamentos<\/strong> (14 aulas)<\/span>\n<ol>\n<li><span style=\"color: #000000\">Produto matriz vetor<br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\">Matrizes ortogonais e unit\u00e1rias<br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\">Normas de vetores e matrizes<br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\">Decomposi\u00e7\u00e3o em Valores Singulares (DVS)<\/span><\/li>\n<\/ol>\n<ol>\n<li style=\"list-style-type: none\"><\/li>\n<\/ol>\n<\/li>\n<li><span style=\"color: #000000\"><strong>Fatora\u00e7\u00e3o QR e Quadrados M\u00ednimos<\/strong> (12 aulas)<\/span>\n<ol>\n<li><span style=\"color: #000000\">Proje\u00e7\u00f5es<br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\">Fatora\u00e7\u00e3o QR<\/span><\/li>\n<li><span style=\"color: #000000\">Ortogonaliza\u00e7\u00e3o de Gram-Schmidt<\/span><\/li>\n<li><span style=\"color: #000000\">Triangulariza\u00e7\u00e3o de Householder<\/span><\/li>\n<li><span style=\"color: #000000\">Problemas de Quadrados M\u00ednimos<\/span><\/li>\n<\/ol>\n<\/li>\n<li><span style=\"color: #000000\"><strong>Condicionamento e Estabilidade<\/strong> (06 aulas)<\/span>\n<ol>\n<li><span style=\"color: #000000\">Condicionamento e n\u00famero de condi\u00e7\u00e3o<\/span><\/li>\n<li><span style=\"color: #000000\">Aritm\u00e9tica de ponto flutuante<\/span><\/li>\n<li><span style=\"color: #000000\">Estabilidade<\/span><\/li>\n<\/ol>\n<\/li>\n<li><span style=\"color: #000000\"><strong>Sistemas de equa\u00e7\u00f5es lineares<\/strong> (04 aulas)<\/span>\n<ol>\n<li><span style=\"color: #000000\">Elimina\u00e7\u00e3o Gaussiana<\/span><\/li>\n<li><span style=\"color: #000000\">Estabilidade da elimina\u00e7\u00e3o Gaussiana<\/span><\/li>\n<li><span style=\"color: #000000\">Decomposi\u00e7\u00e3o de Cholesky<\/span><\/li>\n<\/ol>\n<\/li>\n<li><span style=\"color: #000000\"><strong>Autovalores<\/strong> (12 aulas)<\/span>\n<ol>\n<li><span style=\"color: #000000\">Problema de autovalor<\/span><\/li>\n<li><span style=\"color: #000000\">M\u00e9todo da Pot\u00eancia<\/span><\/li>\n<li><span style=\"color: #000000\">Redu\u00e7\u00e3o a forma de Hessenberg<\/span><\/li>\n<li><span style=\"color: #000000\">Quociente de Rayligh<\/span><\/li>\n<li><span style=\"color: #000000\">Algoritmo QR <\/span><\/li>\n<\/ol>\n<\/li>\n<li><span style=\"color: #000000\"><strong>M\u00e9todos iterativos para sistemas lineares baseados em espa\u00e7os de Krylov<\/strong> (12 aulas)<\/span>\n<ol>\n<li><span style=\"color: #000000\"><span style=\"color: #000000\">M\u00e9todo GMRES (<em>Generalized Minimal Residual Method<\/em>)<\/span><\/span><span style=\"color: #000000\"><br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\">M\u00e9todo dos Gradientes Conjugados<\/span><\/li>\n<li><span style=\"color: #000000\">Precondicionamento<\/span>\n<ol>\n<li style=\"list-style-type: none\"><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h1><span style=\"color: #ff0000\">Metodologia de ensino:<\/span><\/h1>\n<p><span style=\"color: #000000\">Aulas expositivas e de exerc\u00edcios, laborat\u00f3rio e uso de ferramentas computacionais<\/span><\/p>\n<h1><span style=\"color: #ff0000\">Sistema de Avalia\u00e7\u00e3o:<\/span><\/h1>\n<p><span style=\"color: #000000\">Ser\u00e3o aplicados duas provas parciais, um semin\u00e1rio e atividades extras<\/span><\/p>\n<h1><span style=\"color: #ff0000\">Temas de Semin\u00e1rios:<\/span><\/h1>\n<ul>\n<li><\/li>\n<li><\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\">Datas das provas e da entrega dos trabalhos computacionais:<\/span><\/h1>\n<ul>\n<li><span style=\"color: #000000\"><em>Prova 1<\/em>: dia&nbsp; 23 de setembro<br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\"><em>Prova 2<\/em>: dia&nbsp; 25 de novembro<br \/>\n<\/span><\/li>\n<li><span style=\"color: #000000\"><em>Semin\u00e1rios<\/em>:<br \/>\n<\/span><\/li>\n<\/ul>\n<h1><a href=\"https:\/\/nuvem.ufes.br\/index.php\/s\/SG6AWa6KSrZNDoc#pdfviewer\" target=\"_blank\" rel=\"noopener noreferrer\">Acesso \u00e0s&nbsp;aulas&nbsp;para alunos n\u00e3o matriculados na disciplina<\/a><\/h1>\n<h1><span style=\"color: #ff0000\">C\u00e1lculo da m\u00e9dia semestral:<\/span><\/h1>\n<p>A m\u00e9dia semestral (MS) ser\u00e1 dada por<\/p>\n<p>MS = [(P1 + P2)*(0.7\/2) + (T + E)*(0.3\/2)],<\/p>\n<p>onde P1 e P2 s\u00e3o as notas das duas provas, T \u00e9 a nota do trabalho computacional (que corresponde a parte escrita do trabalho e apresenta\u00e7\u00e3o de semin\u00e1rio) e E corresponde \u00e0 notas extras (listas de exerc\u00edcios e outras atividades, a crit\u00e9rio do professor). O aluno ser\u00e1 aprovado sem necessidade de fazer a prova final se MS &gt;= 7.0.<\/p>\n<p>Para os alunos que far\u00e3o a prova final, a M\u00e9dia Final (MF) ser\u00e1<\/p>\n<p>MF = (MS + PF) \/ 2,<\/p>\n<p>onde PF \u00e9 a nota da prova final. O aluno ser\u00e1 aprovado se MF &gt;= 5.0.<\/p>\n<h1><span style=\"color: #ff0000\">Software<\/span><\/h1>\n<ul>\n<li><span style=\"color: #000000\">Matlab, Octave, Phyton, etc<br \/>\n<\/span><\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\">Material de Apoio Did\u00e1tico<\/span><\/h1>\n<ul>\n<li><a href=\"http:\/\/www.cs.utexas.edu\/users\/kincaid\/AMCS251\/\" target=\"_blank\" rel=\"noopener noreferrer\">Curso de \u00c1lgebra Linear Num\u00e9rica do prof. David Kincaid (em ingl\u00eas)<\/a> &#8211; Universidade do Texas em Austin, USA<\/li>\n<li><a href=\"http:\/\/www.cs.utexas.edu\/~dahlin\/professional\/goodTalk.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Giving a conference talk (Mike Dahlin)<\/a><\/li>\n<li><b> <a href=\"http:\/\/www.cs.cornell.edu\/cv\/ShortTalk.htm\"> Short Talk (Charles van Loan)<\/a><\/b><\/li>\n<\/ul>\n<h1><span style=\"color: #ff0000\">Refer\u00eancias Bibliogr\u00e1ficas:<\/span><\/h1>\n<ul>\n<li><span style=\"color: #0000ff\"><span lang=\"en-US\">Lloyd N. Trefethen and D. Bau<\/span>. <i><span lang=\"en-US\">Numerical Linear Algebra<\/span>.<\/i> <span lang=\"en-US\">SIAM (1999)<\/span>.<\/span><\/li>\n<li><span style=\"color: #000000\"><span lang=\"en-US\">R. L, Burden e J. D. Faires<\/span>. <em>An\u00e1lise Num\u00e9rica<\/em>. Cencage Learning, S\u00e3o Paulo, 2008;<\/span><\/li>\n<li><span style=\"color: #000000\"><span lang=\"en-US\">D. Kincaid and W. Cheney.<\/span> <em><span lang=\"en-US\">Numerica Analysis: Mathematics of Scientific Computing<\/span><\/em>. <span lang=\"en-US\">3<\/span><sup><span lang=\"en-US\">rd<\/span><\/sup><span lang=\"en-US\"> Ed, Brooks\/Cole, (2002)<\/span>.<\/span><\/li>\n<li><span style=\"color: #000000\">G.<span lang=\"en-US\"> H. Golub and C. F. Loan. <\/span><span lang=\"en-US\"><em>Matrix Computation<\/em>. Johns Hopkins studies in the mathematical sciences, 1996.<\/span><\/span><\/li>\n<li><span style=\"color: #000000\">Cunha, M.C.C. <em>M\u00e9todos Num\u00e9ricos<\/em>. 2a. <span lang=\"en-US\">Edi\u00e7\u00e3o, 2000.<\/span><\/span><\/li>\n<li><span style=\"color: #000000\"><span lang=\"en-US\">R. A. Horn and C. A. Johnson. <\/span><em><span lang=\"en-US\">Matrix Analysis<\/span><span lang=\"en-US\">. <\/span><\/em><span lang=\"en-US\">Cambridge University Press, 1998<\/span>.<\/span><\/li>\n<li><span style=\"color: #000000\">Dongarra, J.J., Duff, I.S., Sorasen, D.C., Van der Vorst. <em>Numerical Linear Algebra for High-Performance Computers.<\/em> SIAM, 1998.<\/span><\/li>\n<li><span style=\"color: #000000\">L. M. Carvalho, S. Gratton, R. Lago e N. Maculan. <em>\u00c1lgebra Linear Num\u00e9rica e Computacional: m\u00e9todos de Krylov para a solu\u00e7\u00e3o de sistemas lineares<\/em>. Editora Ci\u00eancia Moderna, 2010.<\/span><\/li>\n<li><span style=\"color: #000000\">Kelley C.T. <em>Iterative Methods for Linear and Nonlinear Equations<\/em>. SIAM, 1995.<\/span><\/li>\n<li><span style=\"color: #000000\">Saad, Y. <em>Iterative Methods for Sparse Linear Systems<\/em>. PWS Publishing Company, 1996.<\/span><\/li>\n<li><span style=\"color: #000000\">D. Hanselman e B. Littlefield. <i>MATLAB 6 \u2014 Curso completo.<\/i> Pearson Education do Brasil, S\u00e3o Paulo, 2a edi\u00e7\u00e3o, 2003.<\/span><\/li>\n<li><span style=\"color: #000000\">Cleve Moler. <i><a style=\"color: #000000\" href=\"https:\/\/www.mathworks.com\/moler\/chapters.html\">Numerical Computing with MATLAB<\/a>, 2004.<\/i><\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Objetivo da disciplina: Fornecer ao estudante as ferramentas b\u00e1sicas da \u00e1lgebra linear (num\u00e9rica) para constru\u00e7\u00e3o de algoritmos e m\u00e9todos num\u00e9ricos eficientes. Cursos: Matem\u00e1tica Industrial Hor\u00e1rio das aulas: segundas 10:40 &#8211; 12:20 (Sala 11 &#8211; Eixo 1) e quartas 10:40 &#8211; &hellip; <a href=\"https:\/\/blog.ufes.br\/isaacsantos\/ensino\/algebra-linear-numerica-2018-2\/\">Continue lendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":279,"featured_media":0,"parent":73,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-511","page","type-page","status-publish","hentry"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"post-thumbnail":false,"large-feature":false,"small-feature":false},"uagb_author_info":{"display_name":"Isaac","author_link":"https:\/\/blog.ufes.br\/isaacsantos\/author\/isaac_pinheiro-dos-santos\/"},"uagb_comment_info":0,"uagb_excerpt":"Objetivo da disciplina: Fornecer ao estudante as ferramentas b\u00e1sicas da \u00e1lgebra linear (num\u00e9rica) para constru\u00e7\u00e3o de algoritmos e m\u00e9todos num\u00e9ricos eficientes. Cursos: Matem\u00e1tica Industrial Hor\u00e1rio das aulas: segundas 10:40 &#8211; 12:20 (Sala 11 &#8211; Eixo 1) e quartas 10:40 &#8211; &hellip; Continue lendo &rarr;","_links":{"self":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/511","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/users\/279"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/comments?post=511"}],"version-history":[{"count":29,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/511\/revisions"}],"predecessor-version":[{"id":682,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/511\/revisions\/682"}],"up":[{"embeddable":true,"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/pages\/73"}],"wp:attachment":[{"href":"https:\/\/blog.ufes.br\/isaacsantos\/wp-json\/wp\/v2\/media?parent=511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}