POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATIONS X ± A*X?QA = Q

By V. Hasanov. 2005

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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.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8bc2799861afa1f7394fc4d98812be1b4638541b