Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 73, Issue 12, Pages 2529-2547Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.03.018
Keywords
Generalized coupled Sylvester matrix equations; Conjugate gradient least squares algorithm; Inner product space
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Funding
- National Natural Science Foundation of China [61273194]
- Natural Science Foundation of Anhui Provincial Education Department [KJ2016A458]
- Excellent Personnel Domestic Visiting Project [gxfxZD2016274]
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This paper discusses the conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations Sigma(q)(j=1) A(ij)X(j)B(ij) = F-i, i = 1, 2, . . . ,p. We prove that if this system is consistent then the iterative solution converges to the exact solution and if this system is inconsistent then the iterative solution converges to the least squares solution within the finite iteration steps in the absence of the roundoff errors. Also by setting the initial iterative value properly we prove that the iterative solution converges to the least squares and minimum-norm solution. (C) 2017 Elsevier Ltd. All rights reserved.
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