ON INEXACT NEWTON METHODS FOR SOLVING TWO NONLINEAR MATRIX EQUATIONS*

Karolina Nikolova     Vejdi I. Hasanov

Abstract

In this paper we consider inexact Newton methods for finding the largest positive definite solutions of two nonlinear matrix equations X+ A∗X−1A = Q and X−A∗X−1A = Q, respectively. Using Newton’s method for considered equations requires solving a Stein’s equation at each iteration. For solving the Stein’s equation, we use Smithtype iterations instead of exact methods. Nonlocal convergence of the process is shown. Numerical experiments are included to illustrate the theory.

Keywords: nonlinear matrix equation, positive definite solution, inexact Newton method.

MSC: 65F10, 15A24.

DOI https://doi.org/10.56082/annalsarscimath.2024.2.311

 

Abstract Article                                                                                    Volume 16 no 2 / 2024