Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations
2014 ◽
Vol 2014
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pp. 1-8
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By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equationsAX+YB=CandDX+YE=Fin this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equationAXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm.
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2009 ◽
Vol 50
(7-8)
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pp. 1237-1244
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Keyword(s):
2016 ◽
Vol 40
(1)
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pp. 341-347
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Keyword(s):