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In this paper we study a special case of linearly perturbed discretetime algebraic Riccati equation. We give some sufficient conditions for the existence of a positive definite solution of the considered equation. We propose a basic fixed point iteration and its inversion free variant for finding a positive definite solution. Moreover, by specially choosing the initial value in the basic fixed point iteration we prove that it converges to the largest solution. The theoretical results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

Some existing perturbation bounds for a unique positive definite solution of a nonlinear matrix equation connected to the interpolation theory are analyzed and compared. We examine the behavior of the perturbation bounds, considered in five sources, through experiments with five numerical examples. [ABSTRACT FROM AUTHOR]

In this paper a nonlinear matrix equation is considered. Perturbation estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical examples. [ABSTRACT FROM AUTHOR]

Some perturbation estimates for the unique positive definite solution of a nonlinear matrix equation connected to the interpolation theory are derived. The considered estimations are modification of some existing one. They are obtained by similar transformations of the matrix coefficients with a positive definite matrix. The theoretical results are illustrated by several numerical examples. [ABSTRACT FROM AUTHOR]

We study iterative methods for finding the largest Hermitian positive definite solution of the matrix equation X + ∑ i = 1 m A i ∗ X − 1 A i = Q . Convergence rates of the basic fixed point iteration, inversion free variants of the basic fixed point iteration, and Stein iteration are considered. Some numerical examples are presented to illustrate the convergence behaviour of the various algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Two perturbation estimates of the maximal positive definite solutions to the matrix equations and are considered. These estimates are like to the estimates discussed by Hasanov and Ivanov . The conditions and in are not always satisfied. We replace this conditions by and respective, where P is positive definite matrix. The theoretical results are illustrated by numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper we consider the positive definite solutions of nonlinear matrix equation X + A ⋆ X −δ A = Q, where δ ∈(0,1], which appears for the first time in [S.M. El-Sayed, A.C.M. Ran, On an iteration methods for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001) 632–645]. The necessary and sufficient conditions for the existence of a solution are derived. An iterative algorithm for obtaining the positive definite solutions of the equation is discussed. The error estimations are found. [Copyright &y& Elsevier]

Abstract: The nonlinear matrix equation X − A ∗ X −n A = I is discussed (n is a positive integer). Convergence of the iterative methods proposed by El-Sayed [Comput. Math. Appl. 41 (2001) 579–588] is proved under weaker restrictions for the matrix A and an arbitrary integer n. [Copyright &y& Elsevier]

Abstract: In this paper we investigate nonlinear matrix equations X + A*X −q A = Q and X − A*X −q A = Q where q ∈(0,1]. We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations. We provide a sufficient condition for the equation X + A*X −q A = Q to have two different positive definite solutions and a sufficient condition for the equation X − A*X −q A = Q to have a unique positive definite solution. We also propose iterative methods for obtaining positive definite solutions for these equations. [Copyright &y& Elsevier]