Perturbation bounds for certain matrix expressions and numerical solution of matrix equations. (English)
Margenov, Svetozar (ed.) et al., Numerical analysis and its applications. 4th international conference, NAA 2008, Lozenetz, Bulgaria, June 16‒20, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-00463-6/pbk). Lecture Notes in Computer Science 5434, 68-79 (2009).
Summary: The paper deals with the derivation of improved perturbation bounds for the matrix expression $A_1A_2^{-1}A_3$ and their application to the sensitivity analysis and the solution of fractional-affine matrix equations. An estimate of the overall error in the solution of matrix equations is also given.