Karolina Nikolova†, Vejdi I. Hasanov‡
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
†karolinanikolova@abv.bg Konstantin Preslavsky University of Shumen, Faculty of Mathematics and Informatics, Shumen, Bulgaria
‡v.hasanov@shu.bg Konstantin Preslavsky University of Shumen, Faculty of Mathematics and Informatics, Shumen, Bulgaria
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 16 no 2, 2024
