Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations

Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations

Year:    2018

Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 1 : pp. 140–159

Abstract

The purpose of this paper is to derive the generalized conjugate residual (GCR) algorithm for finding the least squares solution on a class of Sylvester matrix equations. We prove that if the system is inconsistent, the least squares solution can be obtained with infinite iterative steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrix to obtain the minimum norm least squares solutionof the problem. Finally, we give some numerical examples to illustrate the performance of GCR algorithm.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2017-0010

Numerical Mathematics: Theory, Methods and Applications, Vol. 11 (2018), Iss. 1 : pp. 140–159

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Sylvester matrix equation Least squares solution Generalized conjugate residual algorithm Numerical experiments.