Alternately Linearized Implicit Iteration Methods for Solving Quadratic Matrix Equations

Abstract

A numerical solution of the quadratic matrix equations associated with a nonsingular $M$-matrix by using the alternately linearized implicit iteration method is considered. An iteration method for computing a nonsingular $M$-matrix solution of the quadratic matrix equations is developed, and its corresponding theory is given. Some numerical examples are provided to show the efficiency of the new method.