Sensitivity of the matrix equation A 0 +∑ i=1 k σ i A 1 * X p i A i =0,σ i =±1 (original) (raw)

Applied and computational mathematics

Abstract

In this paper, the sensitivity of the solution to the general nonlinear matrix equation A 0 +∑ i=1 k σ i A 1 * X p i A i =0,σ i =±1, is studied, where k is a positive integer, and p i (i=i=11,2,...k) are real numbers. Using the technique of Fréchet derivatives, the perturbed equation is written as an equivalent operator equation, which allows applying the method of Lyapunov majorants and Schauder fixed point principle to obtain norm-wise condition numbers, as well as local and nonlocal perturbation bounds. Several numerical examples are given to illustrate the effectiveness of the perturbation bounds.

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