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An efficient method to compute the Moore–Penrose inverse

An efficient method to compute the Moore–Penrose inverse AbstractA new Schulz-type method to compute the Moore–Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method always converge with fourth-order. A wide set of numerical comparisons of the proposed method with nine higher order methods shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods. For each of sizes n×n{n\times n}and n×(n+10){n\times(n+10)}, n=200,400,600,800,1000,1200{n=200,400,600,800,1000,1200}, ten random matrices were chosen to make these comparisons. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

An efficient method to compute the Moore–Penrose inverse

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6090
eISSN
1869-6090
DOI
10.1515/apam-2016-0064
Publisher site
See Article on Publisher Site

Abstract

AbstractA new Schulz-type method to compute the Moore–Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method always converge with fourth-order. A wide set of numerical comparisons of the proposed method with nine higher order methods shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods. For each of sizes n×n{n\times n}and n×(n+10){n\times(n+10)}, n=200,400,600,800,1000,1200{n=200,400,600,800,1000,1200}, ten random matrices were chosen to make these comparisons.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Apr 1, 2018

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