Location, Separation and Approximation of Solutions for Quadratic Matrix Equations

In this work, we focus on analyzing the location and separation of the solutions of the simplest quadratic matrix equation. For this, we use the qualitative properties that we can deduce of the study of the convergence of iterative processes. This study allow us to determine domains of existence and uniqueness of solutions, and therefore to locate and separate the solutions. Another goal is to approximate a solution of the quadratic matrix equation. For this, we consider iterative processes of fixed point type. So, analyzing the convergence of these iterative processes of fixed point type, we locate, separate and approximate solutions of quadratic matrix equations.