期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 218, 期 7, 页码 3166-3175出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.08.052
关键词
Matrix equations; Iterative method; Minimum-norm solution; Optimal approximation solution; Least-squares solution
资金
- National Natural Science Foundation of China [10971176]
- Hunan Provincial Natural Science Foundation of China [10JJ2002]
In this paper, two iterative algorithms are proposed to solve the linear matrix equations A(1)XB(1) + (C1XD1)-D-T = M-1, A(2)XB(2) + (C2XD2)-D-T = M-2. When the matrix equations are consistent, by the first algorithm, a solution X-psi can be obtained within finite iterative steps in the absence of roundoff-error for any initial value, furthermore, the minimum-norm solution can be got by choosing a special kind of initial matrix. Additionally, the unique optimal approximation solution to a given matrix X-0 can be derived by finding the minimum-norm solution of a new matrix equations A(1)(X) over tildeB(1) + C-1(X) over tilde D-T(1) = M-1, A(2)(X) over tildeB(2) + C-2(X) over tilde D-T(2) = M-2. When the matrix equations are inconsistent, we present the second algorithm to find the least-squares solution with the minimum-norm. Finally, two numerical examples are tested by MATLAB, the results show that these iterative algorithms are efficient. (c) 2011 Elsevier Inc. All rights reserved.
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