2009•Journal of Jiangxi Normal UniversityRequires access

The Symmetric Solution of Matrix Equation and Its Optimal Approximation

LI Qing-chun

Abstract

An iterative method to find the symmetric solution of the linear matrix equation AX+XB=C is put forward in this paper.This iterative method can judgeautomatically the information of solutions.When the equation is consistent,it con-verges a symmetric solution of the equation.When the equation is inconsistent,it converges the least-squares symmetric solution of the equation.More over,for any initial matrix,a symmetric solution can be obtained within finite iteration steps in theabsence of roundoff errors.If a special kind of initial matrix is chosen,the symmetricsolution with least norm can be obtained,which wonderfully handle the problem of solving its optimal approximation solution for a given matrix.

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Key concepts: Mathematics, Matrix (chemical analysis), Symmetric matrix, Iterative method, Matrix difference equation, Applied mathematics, Mathematical analysis, Norm (philosophy)