{"id":332,"date":"2017-09-14T11:02:01","date_gmt":"2017-09-14T14:02:01","guid":{"rendered":"http:\/\/www.professores.uff.br\/diomarcesarlobao\/?page_id=332"},"modified":"2017-09-14T13:44:45","modified_gmt":"2017-09-14T16:44:45","slug":"numerical-methods-metodos-numericos","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/numerical-methods-metodos-numericos\/","title":{"rendered":"Numerical Methods &#8211; Metodos Num\u00e9ricos"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-333\" src=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/300px-Aa222cover.jpg\" alt=\"\" width=\"260\" height=\"260\" srcset=\"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/300px-Aa222cover.jpg 300w, https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/300px-Aa222cover-150x150.jpg 150w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-334\" src=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/300px-Launchvehicle.gif\" alt=\"\" width=\"300\" height=\"238\" \/><\/p>\n<h4><strong>Lesson notes<\/strong><\/h4>\n<ul>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note1.pdf\">Notes 1<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note2.pdf\">Notes 2<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note3.pdf\">Notes 3 (Book)<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note4.pdf\">Notes 4 (Book)<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note5.pdf\">Notes 5<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note6.pdf\">Notes 6 (Book)<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note7.pdf\">Notes 7(Book)<\/a><\/li>\n<li><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/note8.zip\">Notes 8(Book)<\/a><\/li>\n<\/ul>\n<hr \/>\n<h4><strong>See some helpful links<\/strong><\/h4>\n<ul>\n<li>Have a look into<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.ulib.org\/webRoot\/Books\/Numerical_Recipes\/bookfpdf.html\" target=\"_blank\" rel=\"noopener noreferrer\">Numerical Recipes in Fortran<\/a><br \/>\nThe Art of Scientific Computing Second Edition<\/p>\n<p><a href=\"http:\/\/www.mathtools.net\/\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/www.mathtools.net\/<\/a><br \/>\nThe technical computing Portal<br \/>\nfor all you scientific and enginenring needs<\/p>\n<p><a href=\"http:\/\/www.ddj.com\/topics\/scientific\/articles\/\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/www.ddj.com\/topics\/scientific\/articles\/<\/a><br \/>\nScientific Computing<br \/>\nedited by Jeremy Siek(jsiek@lsc.nd.edu)<\/p>\n<p><a href=\"http:\/\/www.cs.fsu.edu\/~mascagni\/papers.html\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/www.cs.fsu.edu\/~mascagni\/papers.html <\/a><br \/>\nDr. Michael Mascagni &#8211; Recent Papers<\/p>\n<p><a href=\"http:\/\/tonic.physics.sunysb.edu\/docs\/num_meth.html\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/tonic.physics.sunysb.edu\/docs\/num_meth.html <\/a><br \/>\nNumerical methods<\/p>\n<p><a href=\"http:\/\/www.math.uic.edu\/~hanson\/mcs471\/float_arithmetic.html\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/www.math.uic.edu\/~hanson\/mcs471\/float_arithmetic.html<\/a><br \/>\nFloating Point Arithmetic Notes<br \/>\nFor MCS 471 Numerical Analysis<\/p>\n<h2 id=\"tablepress-2-name\" class=\"tablepress-table-name tablepress-table-name-id-2\">Home-Page for Official Software<\/h2>\n\n<table id=\"tablepress-2\" class=\"tablepress tablepress-id-2\" aria-labelledby=\"tablepress-2-name\">\n<thead>\n<tr class=\"row-1\">\n\t<th class=\"column-1\">Software\t<\/th><th class=\"column-2\">O.S.\t<\/th><th class=\"column-3\">Language<br \/>\n<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Octave\t<\/td><td class=\"column-2\">Linux \/ Win\t<\/td><td class=\"column-3\">English <br \/>\n<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">Matlab\t<\/td><td class=\"column-2\">Win\t<\/td><td class=\"column-3\">English <br \/>\n<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\">Scilab\t<\/td><td class=\"column-2\">Linux \/ Win\t<\/td><td class=\"column-3\">English <br \/>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-2 from cache -->\n<h2 id=\"tablepress-3-name\" class=\"tablepress-table-name tablepress-table-name-id-3\">Software (Download)<\/h2>\n\n<table id=\"tablepress-3\" class=\"tablepress tablepress-id-3\" aria-labelledby=\"tablepress-3-name\">\n<thead>\n<tr class=\"row-1\">\n\t<th class=\"column-1\">Software<\/th><th class=\"column-2\">Size<br \/>\n<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">Octave for Windows\t<\/td><td class=\"column-2\">9,47 MB<br \/>\n<\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">Turb Pascal 7\t<\/td><td class=\"column-2\">1,74 MB<br \/>\n<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\">Scilab26\t<\/td><td class=\"column-2\">9,76 MB<br \/>\n<br \/>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-3 from cache -->\n<hr \/>\n<h4 style=\"text-align: left;\"><strong>Greek Alphabet<\/strong><\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-351 alignleft\" src=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/Alph_greek.gif\" alt=\"\" width=\"497\" height=\"420\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<h4><strong>FORTRAN<\/strong><\/h4>\n<p><strong>Manuals<\/strong><\/p>\n<ul>\n<li>Professional Programmer&#8217;s Guide to Fortran77, by C. Page &#8211; <a href=\"ftp:\/\/ftp.star.le.ac.uk\/pub\/fortran\/prof77.ps.gz\" target=\"_blank\" rel=\"noopener noreferrer\">PostScrip<\/a>t or <a href=\"ftp:\/\/ftp.star.le.ac.uk\/pub\/fortran\/prof77.tex.gz\" target=\"_blank\" rel=\"noopener noreferrer\">Latex<\/a>.<\/li>\n<li><a href=\"http:\/\/sunsite.unc.edu\/pub\/languages\/fortran\/unfp.html\" target=\"_blank\" rel=\"noopener noreferrer\">Notes on FORTRAN Programming<\/a> &#8211; manual in html for Fortran77.<\/li>\n<li>The same manual in mirrors at: <a href=\"http:\/\/sunsite.icm.edu.pl\/fortran\/unfp.html\" target=\"_blank\" rel=\"noopener noreferrer\">Pol\u00f4nia<\/a> , <a href=\"http:\/\/www.ibiblio.org\/pub\/languages\/fortran\/unfp.html\" target=\"_blank\" rel=\"noopener noreferrer\">US<\/a>, and <a href=\"http:\/\/sunsite.informatik.rwth-aachen.de\/fortran\/\" target=\"_blank\" rel=\"noopener noreferrer\">Alemanha<\/a>.<\/li>\n<li><a href=\"http:\/\/www.fortran.com\/fortran\/F77_std\/rjcnf0001.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran 77<\/a> &#8211; The standard ANSI in html.<\/li>\n<li><a href=\"http:\/\/www.strath.ac.uk\/CC\/Courses\/fortran.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran 77 Notes <\/a>&#8211; Class notes University of Strathclyde, Glasgow.<\/li>\n<li><a href=\"http:\/\/physics.clarku.edu\/sip\/tutorials\/F_tutorial.html\" target=\"_blank\" rel=\"noopener noreferrer\">Introduction to F <\/a>&#8211; A subset of Fortran90.<\/li>\n<\/ul>\n<p><strong>More information<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/www.fortran.com\/fortran\/metcalf.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran Information<\/a>, webpage held by M. Metcalf (CERN).<\/li>\n<li><a href=\"http:\/\/climate.gsfc.nasa.gov\/~pincus\/F90\/\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran 90 Home<\/a>, to those who want learn Fortran 90.<\/li>\n<li><a href=\"http:\/\/www.nsc.liu.se\/~boein\/fortran.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran 90<\/a>, webpage at NSC<\/li>\n<li><a href=\"http:\/\/www.kcl.ac.uk\/kis\/support\/cc\/fortran\/f90home.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran 90\/95<\/a>, webpage at Kings College London.<\/li>\n<li><a href=\"http:\/\/www.fortran.com\/fortran\/tutorials.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran Tutorials:<\/a> manuals list on-line.<\/li>\n<li><a href=\"http:\/\/www.fortran.com\/fortran\/Books\/books.html\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran Books:<\/a> Books list, some are free&#8230;<\/li>\n<li><a href=\"http:\/\/www.fortran.com\/fortran\/\" target=\"_blank\" rel=\"noopener noreferrer\">Fortran Market<\/a>: products, services and information about Fortran.<\/li>\n<\/ul>\n<hr \/>\n<p><strong>Other suggested links<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/www.impa.br\/\" target=\"_blank\" rel=\"noopener noreferrer\">IMPA-Instituto de Matem\u00e1tica Pura e Aplicada<\/a><\/li>\n<li><a href=\"http:\/\/www.somatematica.com.br\/\" target=\"_blank\" rel=\"noopener noreferrer\">S\u00f3 Matem\u00e1tica<\/a><\/li>\n<li><a href=\"http:\/\/www.dma.uem.br\/kit\" target=\"_blank\" rel=\"noopener noreferrer\">Algumas coisinhas sobre c\u00e1lculo e \u00e1lgebra<\/a><\/li>\n<li><a href=\"http:\/\/www.winedt.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">Everything about Latex (or Miktex or Tex)<\/a><\/li>\n<li><a href=\"http:\/\/www.sbmac.org.br\/\" target=\"_blank\" rel=\"noopener noreferrer\">SBMAC-Sociedade Brasileira de Matem\u00e1tica Aplicada e Computacional<\/a><\/li>\n<li><a href=\"http:\/\/www.lncc.br\/\" target=\"_blank\" rel=\"noopener noreferrer\">LNCC-Laborat\u00f3rio Nacional de Computa\u00e7\u00e3o Cient\u00edfica<\/a><\/li>\n<li><a href=\"http:\/\/www.del.ufms.br\/tutoriais\" target=\"_blank\" rel=\"noopener noreferrer\">Tutorial sobre o Matlab<\/a><\/li>\n<li><a href=\"http:\/\/www.toolscenter.org\/\" target=\"_blank\" rel=\"noopener noreferrer\">Editor for Tex (free)<\/a><\/li>\n<li><a href=\"http:\/\/mathworld.wolfram.com\/topics\/NumericalIntegration.html\" target=\"_blank\" rel=\"noopener noreferrer\">Methods for Numerical Integration<\/a><\/li>\n<li><a href=\"http:\/\/homepages.borland.com\/efg2lab\/Library\/Delphi\/MathFunctions\/index.html\" target=\"_blank\" rel=\"noopener noreferrer\">Mathematics for Delphi<\/a><\/li>\n<li><a href=\"http:\/\/www.calc101.com\/webMathematica\/MSP\/Calc101\/WalkD\" target=\"_blank\" rel=\"noopener noreferrer\">Derivative on-line<\/a><\/li>\n<\/ul>\n<hr \/>\n<p><strong><span style=\"font-size: large;\">MATLAB<\/span><\/strong><\/p>\n<p><strong><span style=\"font-size: small;\">Try this Link for more MATLAB infos&#8230;<\/span><\/strong><span style=\"font-family: Arial;\"><br \/>\n<\/span>Click on <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/matlab_tools\/\">website<\/a><\/p>\n<p>The MATLAB Teaching Codes consist of 37 short, text files containing MATLAB commands for performing basic linear algebra computations.These Teaching Codes are available as a single tar file, or as individual text files. You can download the Codes to your computer in two different ways.<\/p>\n<p>[1] To Download The Teaching Codes As A Single Tar File<br \/>\n(a) Click on <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/Tcodes.tar_.gz\">Tcodes.tar<\/a> to access the tar file.<br \/>\n(b) With most browsers (Netscape, Explorer) a dialog box now appears,<br \/>\nand you can specify in which directory to save the tar file.<br \/>\n(c) Within a terminal window, move to the specified directory and<br \/>\nunpack the tar file by typing the command:<\/p>\n<p>tar xvf Tcodes.tar<br \/>\n<span style=\"font-family: Arial;\"><br \/>\n<\/span>A new directory called Tcodes is created, and it contains all of the<br \/>\nMATLAB Teaching Codes.<\/p>\n<p>[2] To View Or Download A Particular Teaching Code<\/p>\n<p>The name of each MATLAB Teaching Code is listed below.<br \/>\nTo VIEW a particular Teaching Code: click on its name.<br \/>\nTo DOWNLOAD a particular Teaching Code: click on its name, then use<br \/>\nthe menus on your Web browser to save the file to your computer.<br \/>\nFor example, most browsers (Netscape, Explorer) have a FILE menu.<br \/>\nUnderneath the FILE menu is a SAVE command that you can select.<br \/>\nUsually, a dialog box then appears and you can specify in which<br \/>\ndirectory you wish to save the text file.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/cab-m\/\">cab.m<\/a>&#8230;&#8230;&#8230;&#8230;Echelon factorization A = c a b.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/cofactor-m\/\">cofactor.m<\/a>&#8230;&#8230;..Matrix of cofactors.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/colbasis-m\/\">colbasis.m<\/a>&#8230;&#8230;..Basis for the column space.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/cramer-m\/\">cramer.m.<\/a>&#8230;&#8230;&#8230;..Solve the system Ax=b.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/determ-m\/\">determ.m<\/a>&#8230;&#8230;..Matrix determinant from plu.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/eigen2-m\/\">eigen2.m.<\/a>&#8230;&#8230;&#8230;..Characteristic polynomial, eigenvalues, eigenvectors.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/eigshow-m\/\">eigshow.m<\/a>&#8230;&#8230;&#8230;&#8230;Graphical demonstration of eigenvalues and singular values.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/eigval-m\/\">eigval.m.<\/a>&#8230;&#8230;&#8230;..Eigenvalues and their algebraic multiplicity.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/eigvec-m\/\">eigvec.m<\/a>&#8230;&#8230;&#8230;&#8230;Eigenvectors and their geometric multiplicity.<\/p>\n<p><a href=\"#\">elim.m<\/a>&#8230;&#8230;&#8230;&#8230;EA=R factorization.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/findpiv-m\/\">findpiv.m<\/a>&#8230;&#8230;&#8230;&#8230;Used by plu to find a pivot for Gaussian elimination.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/fourbase-m\/\">fourbase.m<\/a>&#8230;&#8230;&#8230;&#8230;Bases for all 4 fundamental subspaces.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/grams-m\/\">grams.m<\/a>&#8230;&#8230;&#8230;&#8230;Gram-Schmidt orthogonalization of the columns of A.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/house-m\/\">house.m<\/a>&#8230;&#8230;&#8230;&#8230;Stores the &#8220;house&#8221; data set in X.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/inverse-m\/\">inverse.m<\/a>&#8230;&#8230;&#8230;&#8230;Matrix inverse by Gauss-Jordan elimination.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/leftnull-m\/\">leftnull.m<\/a>&#8230;&#8230;&#8230;&#8230;Basis for the left nullspace.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/linefit-m\/\">linefit.m<\/a>&#8230;&#8230;&#8230;&#8230;Plot the least squares fit by a line.<\/p>\n<p><a href=\"#\">lsq.m<\/a>&#8230;&#8230;&#8230;&#8230;Least squares solution of Ax=b.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/normal-m\/\">normal.m<\/a>&#8230;&#8230;&#8230;&#8230;Eigenvalues and eigenvectors of a normal matrix A.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/nulbasis-m\/\">nulbasis.m<\/a>&#8230;&#8230;&#8230;&#8230;Basis for the nullspace.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/orthcomp-m\/\">orthcomp.m<\/a>&#8230;&#8230;&#8230;&#8230;Orthogonal complement of a subspace.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/partic-m\/\">partic.m<\/a>&#8230;&#8230;&#8230;&#8230;Particular solution of Ax=b.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/plot2d-m\/\">plot2d.m<\/a>&#8230;&#8230;&#8230;&#8230;Two dimensional plot.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/plu-m\/\">plu.m<\/a>&#8230;&#8230;&#8230;&#8230;Rectangular PA=LU factorization *with row exchanges*.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/poly2str-m\/\">poly2str.m<\/a>&#8230;&#8230;&#8230;&#8230;Convert a polynomial coefficient vector to a string.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/project-m\/\">project.m<\/a>&#8230;&#8230;&#8230;&#8230;Project a vector b onto the column space of A.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/projmat-m\/\">projmat.m<\/a>&#8230;&#8230;&#8230;&#8230;Projection matrix for the column space of A.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/randperm-m\/\">randperm.m<\/a>&#8230;&#8230;&#8230;&#8230;Random permutation.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rowbasis-m\/\">rowbasis.m<\/a>&#8230;&#8230;&#8230;&#8230;Basis for the row space.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/samespan-m\/\">samespan.m<\/a>&#8230;&#8230;&#8230;&#8230;Test if two matrices have the same column space.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/signperm-m\/\">signperm.m<\/a>&#8230;&#8230;&#8230;&#8230;Determinant of the permutation matrix with rows ordered by p.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/slu-m\/\">slu.m<\/a>&#8230;&#8230;&#8230;&#8230;LU factorization of a square matrix using *no row exchanges*.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/splu-m\/\">splu.m<\/a>&#8230;&#8230;&#8230;&#8230;Square PA=LU factorization *with row exchanges*.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/splv-m\/\">splv.m<\/a>&#8230;&#8230;&#8230;&#8230;Solution to a square, invertible system.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/symmeig-m\/\">symmeig.m<\/a>&#8230;&#8230;&#8230;&#8230;Eigenvalues and eigenvectors of a symmetric matrix.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/tridiag-m\/\">tridiag.m<\/a>&#8230;&#8230;&#8230;&#8230;Tridiagonal matrix.<\/p>\n<hr \/>\n<ul>\n<li>MacLaurin Series &amp; Convergence<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/signperm-m\/\">sinecomp.m<\/a><\/p>\n<p>compares MATLAB sin(x) with <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/mysine-m\/\">mysine.m<\/a> (which uses <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/factorl-m\/\">factorl.m<\/a>)<\/p>\n<ul>\n<li>Root Finding<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/incsrch-m\/\">incsrch.m<\/a><\/p>\n<p>root finding by incremental search requires <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/func1-m\/\">func1.m<\/a><\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/bisect-m\/\">bisect.m<\/a><\/p>\n<p>bisection root finding code; uses function file: <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/fcn_nr-m\/\">fcn.m<\/a><\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/falspos-m\/\">falspos.m<\/a><\/p>\n<p>root finding by false position<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/newtraph-m\/\">newtraph.m<\/a><\/p>\n<p>Newton-Raphson root finding code; makes use of <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/fcn_nr-m\/\">fcn_nr.m<\/a><\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/secant-m\/\">secant.m<\/a><\/p>\n<p>root finding by secant method<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/onepoint-m\/\">onepoint.m<\/a><\/p>\n<p>one-point iteration root finding<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/oneptrx-m\/\">oneptrx.m<\/a><\/p>\n<p>root finding by one point iteration with relaxation<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/oneptrlx-m\/\">oneptrlx.m<\/a><\/p>\n<p>one-point iteration root finding with relaxation and plotting of optimal relaxation value. Plotting requires: <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/quickplt-m\/\">quickplt.m<\/a><\/p>\n<ul>\n<li>Non-Linear Equation Solving<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/jacobi-m\/\">jacobi.m<\/a><\/p>\n<p>Jacobi Iteration &#8211; Method of Simultaneous Displacement for a system of linear equations; requires: <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g1-m\/\">lin_g1.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g2-m\/\">lin_g2.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g3-m\/\">lin_g3.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g4-m\/\">lin_g4.m<\/a><\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/gs-m\/\">gs.m<\/a><\/p>\n<p>Gauss-Seidel iteration for system of linear equations requires: <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g1-m\/\">lin_g1.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g2-m\/\">lin_g2.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g3-m\/\">lin_g3.m<\/a>,<a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g4-m\/\">lin_g4.m<\/a><\/p>\n<p><a href=\"http:\/\/www.meusiteantigo.uff.br\/diomar_cesar_lobao\/material\/Matlab_codes\/Matlab_codes01\/gssor.m\">gssor.m<\/a><\/p>\n<p>Gauss-Seidel iteration with relaxation (linear equations) requires: <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g1-m\/\">lin_g1.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g2-m\/\">lin_g2.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g3-m\/\">lin_g3.m<\/a>,<a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/lin_g4-m\/\">lin_g4.m<\/a><\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/gssornl-m\/\">gssornl.m<\/a><\/p>\n<p>Gauss-Seidel iteration with relaxation (nonlinear equations)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/gausseid-m\/\">gausseid.m<\/a><\/p>\n<p>Gauss-Seidel non-linear equation solving with relaxation; uses function files <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/g1-m\/\">g1.m<\/a> and <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/g2-m\/\">g2.m<\/a><\/p>\n<ul>\n<li>Linear Equation Solving<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/gauselim-m\/\">gauselim.m<\/a><\/p>\n<p>Gaussian elimination routine, single RHS, (needs gepivot.m)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/gausjord-m\/\">gausjord.m<\/a><\/p>\n<p>Gauss-Jordan routine, single RHS, (needs gepivot.m)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/gepivot-m\/\">gepivot.m<\/a><\/p>\n<p>partial pivoting routine for gauselim.m, gausdem.m, and gausjord.m<\/p>\n<ul>\n<li>Interpolation<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/splineex-m\/\">splineex.m<\/a><\/p>\n<p>spline\/polynomial interpolation example. This example makes use of the polyint.m function.<\/p>\n<ul>\n<li>Integration<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/trapint-m\/\">trapzeq.m<\/a><\/p>\n<p>integration using trapezoidal rule (equally spaced data)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/trapint-m\/\">trapint.m<\/a><\/p>\n<p>integration using trapezoidal rule (unequally spaced data)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/traptoltol-m\/\">traptoltol.m<\/a><\/p>\n<p>integration using trapezoidal rule to specified tolerance<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/simpson-m\/\">simpson.m<\/a><\/p>\n<p>use MATLAB&#8217;s symbolic features to derive Simpson&#8217;s 1\/3 integration rule<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/simptol-m\/\">simptol.m<\/a><\/p>\n<p>integration using Simpsons 1\/3 rule to specified tolerance<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/simp0-m\/\">simp0.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/simp1-m\/\">simp1.m<\/a>, <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/simp2-m\/\">simp2.m<\/a>:<\/p>\n<p>various versions Simpson&#8217;s Integration Rule. See the file<a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/simpdemo-m\/\"> simpdemo.m<\/a> for an example of calling the simp0.m routine. simpdemo.out lists the output of simpdemo.m.<\/p>\n<ul>\n<li>Initial Value ODE Solutions<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/odeeuler-m\/\">odeeuler.m<\/a><\/p>\n<p>ODE solution using Euler&#8217;s method<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/odeeuler-m\/\">odefunc1.m<\/a><\/p>\n<p>right hand side of first order ODE<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/odesmd-m\/\">odesmd.m<\/a><\/p>\n<p>right hand side of second order ODE corresponding to a spring-mass-damper<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/eusquare-m\/\">eusquare.m<\/a><\/p>\n<p>Matlab code for Euler solution of a spring-mass-damper system excited by a square wave.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rk4demo-m\/\">rk4demo.m<\/a><\/p>\n<p>demonstration of a three solution methods to a first order ODE&#8230;<\/p>\n<ul>\n<li>\n<ol>\n<li>Euler<\/li>\n<li>Classical RK4<\/li>\n<li>Matlab&#8217;s ode45<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p>This program requires the function file: <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/fcn1-m\/\">fcn1.m<\/a>.<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rhs_smd-m\/\">rhs_smd.m<\/a><\/p>\n<p>right hand side for spring-mass-damper ODE (see rk4ode2.m and rk4ada2.m)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rhs_vdp-m\/\">rhs_vdp.m<\/a><\/p>\n<p>right hand side for Van Der Pol&#8217;s ODE (see rk4ode2.m and rk4ada2.m)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rk4ada-m\/\">rk4ada.m<\/a><\/p>\n<p>adaptive 4th order Runge-Kutta (first order ODE)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rk4ada2-m\/\">rk4ada2.m<\/a><\/p>\n<p>adaptive 4th order Runge-Kutta (second order ODE) for spring-mass-damper or Van Der Pol&#8217;s equation (see functions rhs_smd.m and rhs_vdp.m)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rk4ada-m\/\">rk4ada.m<\/a><\/p>\n<p>4th order Runge-Kutta (first order ODE)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rk4ode2-m\/\">rk4ode2.m<\/a><\/p>\n<p>4th order Runge-Kutta (second order ODE) for spring-mass-damper or Van Der Pol&#8217;s equation (see functions rhs_smd.m and rhs_vdp.m)<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/rksquare-m\/\">rksquare.m<\/a><\/p>\n<p>Matlab code for Runge-Kutta solution of a spring-mass-damper system excited by a square wave. Two solutions are presented here:<\/p>\n<ul>\n<li>\n<ol>\n<li>One makes use of a classical implementation of a 4th order Runge-Kutta method using the function file <a href=\"http:\/\/www.meusiteantigo.uff.br\/diomar_cesar_lobao\/material\/Matlab_codes\/Matlab_codes01\/smdrk4.m\">smdrk4.m<\/a>.<\/li>\n<li>The second solution uses the one line call to the built-in Matlab function ode45. It uses the more complicated function file <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/smdode45-m\/\">smdode45.m<\/a>.<\/li>\n<li>Take a look at the <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/rksquare.gif\">output<\/a> of rksquare.m.<\/li>\n<\/ol>\n<\/li>\n<li>Boundary Value ODE&#8217;s<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/shooting-m\/\">shooting.m<\/a><\/p>\n<p>Shooting Method demo code<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/finitedf-m\/\">finitedf.m<\/a><\/p>\n<p>Finite Difference demo code<\/p>\n<ul>\n<li>Eigen-value problems<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/power-m\/\">power.m<\/a><\/p>\n<p>Power method of solution for highest\/lowest eigen value. <a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/results-of-this-program\/\">Results of this program<\/a>.<\/p>\n<ul>\n<li>Signal Processing<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/fft_plot-m\/\">fft_plot.m<\/a><\/p>\n<p>routine to take the Fourier transform of a signal and plot both the time and frequency domain representations. Typical use:<\/p>\n<p>&gt;&gt; n\u00a0 = 100;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % number of data points\u00a0 &gt;&gt; dt = 0.01;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % spacing between samples\u00a0 &gt;&gt; t\u00a0 = 0:dt:(n-1)*dt;\u00a0 % time vector\u00a0 &gt;&gt; y\u00a0 = sin(2*pi*10*t); % 10 Hz sin wave\u00a0 &gt;&gt; fft_plot(y,dt);\u00a0\u00a0\u00a0\u00a0\u00a0 % plot of signal in time and frequency domain<\/p>\n<h2>Misc. Programs<\/h2>\n<ul>\n<li>Matlab Matrix Examples<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/matrix-out\/\">matrix.out<\/a><\/p>\n<p>examples of using MATLAB&#8217;s various matrix operators<\/p>\n<ul>\n<li>Plotting<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/supertitle-m\/\">supertitle.m<\/a><\/p>\n<p>plot a main or super title above a series of subplots<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/quickplt-m\/\">quickplt.m<\/a><\/p>\n<p>plotting function with labeling and titles<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/fcn2plot-m\/\">fcn2plot.m<\/a><\/p>\n<p>utility file to plot two functions simultaneously<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/irrarea-m\/\">irrarea.m<\/a><\/p>\n<p>area of an irregular closed contour<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/makshape-m\/\">makshape.m<\/a><\/p>\n<p>a simple program for digitizing an irregular shape<\/p>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/viewdir-m\/\">viewdir.m<\/a><\/p>\n<p>utility for on-screen control of view direction in 3D plots<\/p>\n<ul>\n<li>Matlab Format Strings<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/splitstr-m\/\">splitstr.m<\/a><\/p>\n<p>an example of splitting long format strings in Matlab fprintf statements<\/p>\n<ul>\n<li>Matlab Bundle M-Scripts<\/li>\n<\/ul>\n<p><a href=\"http:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-content\/uploads\/sites\/85\/2017\/09\/Matlab_ExamplesBundle.zip\">Matlab_ExamplesBundle.zip<\/a> Matlab Example Bundle<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Lesson notes Notes 1 Notes 2 Notes 3 (Book) Notes 4 (Book) Notes 5 Notes 6 (Book) Notes 7(Book) Notes 8(Book) See some helpful links Have a look into Numerical Recipes in Fortran The Art of Scientific Computing Second Edition http:\/\/www.mathtools.net\/ The technical computing Portal for all [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-332","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/comments?post=332"}],"version-history":[{"count":22,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/332\/revisions"}],"predecessor-version":[{"id":587,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/332\/revisions\/587"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/media?parent=332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/categories?post=332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/tags?post=332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}