An Iterative Algorithm for Maximal and Minimal Solutions of a Class Matrix Equations

Abstract

In the paper, the peak solutions of a class equation is studied, the peak solutions are the maximal and minimal solutions. There is an iterative algorithm given for the solutions of the class equation. First, the existence of the peak solutions of the class equations is obtained. Second, when the peak solutions exist, an iterative algorithm is established to converge to the peak solutions of the class equation. By an upper bound and a lower bound of the solutions of the equation solution as the initial matrix, the iterative algorithm of the paper converges to the peak solutions of the class equation. The convergence problem of the algorithm is proved by the mathematical induction in the paper. The above results are verified by the examples.