AN ITERATIVE METHOD TO SOLVE SYMMETRIC POSITIVE DEFINITE MATRIX EQUATIONS

作者：Salkuyeh Davod Khojasteh^*; Beik Fatemeh Panjeh Ali

来源：Mathematical Reports, 2014, 16(2): 271-283.

• linear operator
• symmetric positive definite
• matrix equation
• iterative method
• convergence

Let A : R-mxn -> R-mxn be a symmetric positive definite linear operator. In this paper, we propose an iterative algorithm to solve the general matrix equation A(X) = C which includes the Lyapunov matrix equation and Sylvester matrix equation as special cases. It is proved that the sequence of the approximate solutions, obtained by the presented algorithm, satisfies an optimality condition. More precisely, the application of the proposed method is investigated for solving the Sylvester matrix equation S(X) = C, where S is the well-known Sylvester operator S(X) = AX + XB. In order to illustrate the effectiveness of the algorithm, two numerical examples are given.

• 出版日期2014