A note on the iterative solutions of general coupled matrix equation |
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Authors: | Jian-Jun Zhang |
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Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, China |
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Abstract: | Recently, Ding and Chen F. Ding, T. Chen, On iterative solutions of general coupled matrix equations, SIAM J. Control Optim. 44 (2006) 2269-2284] developed a gradient-based iterative method for solving a class of coupled Sylvester matrix equations. The basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified, so that the iterative solutions are obtained by applying hierarchical identification principle. In this note, by considering the coupled Sylvester matrix equation as a linear operator equation we give a natural way to derive this algorithm. We also propose some faster algorithms and present some numerical results. |
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Keywords: | Matrix equations Gradient search principle Krylov subspace Iterative Convergence |
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