Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 353, Issue 13, Pages 3233-3248Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2016.06.008
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The symmetric solutions of linear matrix equations are extensively required in mathematics and engineering problems. The purpose of this paper is on deriving the biconjugate residual (BCR) algorithm for finding the least Frobenius norm symmetric solution pair (X, Y) of the coupled generalized Sylvester matrix equations {A(1)XB(1) + C1XD1 + E1YF1 = G(1), A(2)XB(2) + C2XD2 + E-2 YF2 = G(2). The convergence analysis shows that the BCR algorithm can compute the least Frobenius norm symmetric solution pair of the coupled generalized Sylvester matrix equations within a finite number of iterations in the absence of round-off errors. Finally, we give three numerical examples to illustrate the performance of the BCR algorithm. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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