Year: 2024
Type: article
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 Smith type iterations instead of exact methods. Nonlocal convergence of the process is shown. Numerical experiments are included to illustrate the theory.
Authors: Karolina Nikolova, Vejdi I. Hasanov
Institution: Shumen University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4404113864