期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 197, 期 1, 页码 41-50出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2007.07.040
关键词
matrix equations; gradient search principle; Jacobi iteration; Gauss-Seidel iteration; hierarchical identification principle
In this paper, by extending the well-known Jacobi and Gauss-Seidel iterations for Ax = b, we study iterative solutions of matrix equations AXB = F and generalized Sylvester matrix equations AXB + CXD = F ( including the Sylvester equation AX + XB = F as a special case), and present a gradient based and a least-squares based iterative algorithms for the solution. It is proved that the iterative solution always converges to the exact solution for any initial values. The basic idea is to regard the unknown matrix X to be solved as the parameters of a system to be identified, and to obtain the iterative solutions by applying the hierarchical identification principle. Finally, we test the algorithms and show their effectiveness using a numerical example. (C) 2007 Elsevier Inc. All rights reserved.
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