Iteration with Stepsize Parameter and Condition Numbers for a Nonlinear Matrix Equation

Main Article Content

Syed M. Raza Shah Naqvi
Jie Meng
Hyun-Min Kim


In this paper, the nonlinear matrix equation $X^p+A^TXA=Q$, where $p$ is a positive integer, $A$ is an arbitrary $n\times n$ matrix, and $Q$ is a symmetric positive definite matrix, is considered. A fixed-point iteration with stepsize parameter for obtaining the symmetric positive definite solution of the matrix equation is proposed. The explicit expressions of the normwise, mixed and componentwise condition numbers are derived. Several numerical examples are presented to show the efficiency of the proposed iterative method with proper stepsize parameter and the sharpness of the three kinds of condition numbers.

Article Details


Most read articles by the same author(s)