Vejdi I. Hasanov†
Abstract: In this paper we study a special case of linearly perturbed discretetime algebraic Riccati equation. We give some su cient conditions for the existence of a positive de nite solution of the considered equation. We propose a basic xed point iteration and its inversion free variant for nding a positive de nite solution. Moreover, by specially choosing the initial value in the basic xed point iteration we prove that it converges to the largest solution. The theoretical results are illustrated by numerical examples.
MSC: 65F10; 15A24
keywords: nonlinear matrix equation, positive de nite solution, iterative method
DOI 10.56082/annalsarscimath.2021.1-2.5
†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 13 no 1-2, 2021
