求矩阵方程AXB+CXD=F的中心对称最小二乘解的迭代算法

Abstract

Abstract:

An iterative method is presented to solve the minimum Frobenius norm residual problem: min AXB+CXD-F with unknown centrosymmetric matrix X. By this iterative method, for any initial centrosymmetric matrix X₀, a solution X* can be obtained automatically within finite iteration steps in the absence of roundoff errors, and the solution X* with least Frobenius norm can be obtained by choosing a special initial centrosymmetric matrix. In addition, its optimal approximation matrix to a given matrix can be obtained. Numerical examples are given to show that the intertive method is quite efficient.

Key words: Matrix equation, Centrosymmetric matrix, Least squares solution, Least-norm solution, Iterative method, Optimal approximation

CLC Number:

15A24

SHANG Li-Na, ZHANG Kai-Yuan. An Iterative Method for the Least Squares Centrosymmetric Solution of the Matrix Equation AXB+CXD=F[J].Acta mathematica scientia,Series A, 2010, 30(3): 776-783.

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An Iterative Method for the Least Squares Centrosymmetric Solution of the Matrix Equation AXB+CXD=F

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