On two perturbation estimates of the extreme solutions to the equations X ± A*X−1A = Q☆

By V. Hasanov, I. Ivanov. 2006

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Abstract Two perturbation estimates for maximal positive definite solutions of equations X  +  A * X −1 A  =  Q and X  −  A * X −1 A  =  Q are considered. These estimates are proved in [Hasanov et al., Improved perturbation Estimates for the Matrix Equations X  ±  A * X −1 A  =  Q , Linear Algebra Appl. 379 (2004) 113–135]. We derive new perturbation estimates under weaker restrictions on coefficient matrices of the equations. The theoretical results are illustrated by numerical examples.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Numerical Analysis

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