Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X∧−C)−1A

Dongjie Gao

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We consider the nonlinear matrix equation X=Q+A∗(X∧−C)−1A, where Q is positive definite, C is positive semidefinite, and X∧ is the block diagonal matrix defined by X∧=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given.

Date: 2013
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https://doi.org/10.1155/2013/216035

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:216035

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