Perturbation analysis of the matrix equation X - ∑_i=1^m A_i^* X^p_i A_i = Q

2012/08/17 by Jing Li, Li, Jing
Computer Science · Mathematics · Physics and Astronomy · #15A24 #47H14 #65H05 #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1208.3518

openalex publication_date 2012/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Consider the nonlinear matrix equation X-sum_i=1^mA_i^*X^p_iA_i=Q with p_i>0. Sufficient and necessary conditions for the existence of positive definite solutions to the equation with p_i>0 are derived. Two perturbation bounds for the unique solution to the equation with 0

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