Solutions of a class of nonlinear matrix equations

2019/07/19 by Samik Pakhira, Pakhira, Samik, Snehasish Bose +3
Computer Science · Mathematics · #15A24 #47H09 #47H10 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Mathematics and Applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1907.08408

openalex publication_date 2019/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 X^s + 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.

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