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.