On iterative schemes for matrix equations

Abstract

In this work we focus on solving quadratic matrix equations. We start by transforming the quadratic matrix equation into a fixed point equation. From this transformation, we propose an iterative scheme of stable successive approximations. We study the global convergence of this iterative scheme. In addition, we obtain a result of restricted global convergence to the well-known Picard method using a technique of auxiliary points. From the results obtained, we analyze the location and separation of the solutions of the quadratic matrix equation considered. Finally, we build a hybrid iterative scheme, predictor-corrector, which allow us to approximate a solution of the quadratic matrix equation more efficiently.