Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 140-159.
Published online: 2018-11
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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.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0010}, url = {http://global-sci.org/intro/article_detail/nmtma/10647.html} }
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.