Linear Algebra: New Applications
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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 24 Jul 2014 02:06:01 GMTThu, 24 Jul 2014 02:06:01 GMTNew applications in the Linear Algebra categoryhttp://www.mapleprimes.com/images/mapleapps.gifLinear Algebra: New Applications
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Internet Page Ranking Algorithms
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In this guest article in the Tips and Techniques series, Dr. Michael Monagan explains how internet pages are ranked.<img src="/view.aspx?si=153532/thumb.jpg" alt="Internet Page Ranking Algorithms" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan explains how internet pages are ranked.153532Thu, 20 Mar 2014 04:00:00 ZProf. Michael MonaganProf. Michael MonaganApplication of the Modified Gram-Schmidt Algorithm
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<p>Maple's QRDecomposition command basically utilizes one of two routines for generating the Q and R matrices. If the matrix contains only integers and/or symbolic expressions, then Maple performs a QR decomposition using the Classical Gram-Schmidt algorithm. If however, the matrix contains a mixture of integers and floating point decimals or only floating point decimals, then Maple carries out the QR decomposition of the matrix using Householder transformations. My approach below uses a third alternative, the Modified Gram-Schmidt algorithm, which I read about in Chapter 8 of the textbook, NUMERICAL LINEAR ALGEBRA, by Lloyd N. Trefethen and David Bau III.</p><img src="/view.aspx?si=152382/05160ad08a75a6b7948e889b5999f0ea.gif" alt="Application of the Modified Gram-Schmidt Algorithm" align="left"/><p>Maple's QRDecomposition command basically utilizes one of two routines for generating the Q and R matrices. If the matrix contains only integers and/or symbolic expressions, then Maple performs a QR decomposition using the Classical Gram-Schmidt algorithm. If however, the matrix contains a mixture of integers and floating point decimals or only floating point decimals, then Maple carries out the QR decomposition of the matrix using Householder transformations. My approach below uses a third alternative, the Modified Gram-Schmidt algorithm, which I read about in Chapter 8 of the textbook, NUMERICAL LINEAR ALGEBRA, by Lloyd N. Trefethen and David Bau III.</p>152382Tue, 01 Oct 2013 04:00:00 ZDouglas LewitDouglas Lewit