Solution of a Class of Nonlinear Matrix Equations

Article Type

Research Article

Publication Title

Bulletin of the Iranian Mathematical Society

Abstract

In this article, we present several necessary and sufficient conditions for the existence of Hermitian positive definite solutions of nonlinear matrix equations of the form Xs+ A∗X-tA+ B∗X-pB= Q, where s, t, p≥ 1 , A, B are nonsingular matrices and Q is a Hermitian positive definite matrix. We derive some iterations to compute the solutions followed by some examples. In this context, we also discuss about the maximal and the minimal Hermitian positive definite solution of this particular nonlinear matrix equation.

First Page

415

Last Page

434

DOI

10.1007/s41980-020-00391-9

Publication Date

4-1-2021

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