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Volume 11, Issue 1
Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations

Baohua Huang & Changfeng Ma

DOI: 10.4208/nmtma.OA-2017-0010

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 140-159.

Published online: 2018-11

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-11-140, author = {Baohua Huang and Changfeng Ma}, title = {Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0010}, url = {http://global-sci.org/intro/article_detail/nmtma/10647.html} }
TY - JOUR T1 - Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations AU - Baohua Huang & Changfeng Ma JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 140 EP - 159 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0010 UR - https://global-sci.org/intro/article_detail/nmtma/10647.html KW - Sylvester matrix equation, Least squares solution, Generalized conjugate residual algorithm, Numerical experiments. AB -

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.

Baohua Huang and Changfeng Ma. (2018). Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations. Numerical Mathematics: Theory, Methods and Applications. 11 (1). 140-159. doi:10.4208/nmtma.OA-2017-0010
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