Title: Residual bounds of the nonlinear matrix equation X + A*F(X)A = Q

Authors: Ivan Popchev; Vera Angelova

Addresses: Department of Intelligent Systems, Institute of Information and Communication Technologies, Akad. G. Bonchev, bl. 2, Sofia 1113, Bulgaria ' Department of Intelligent Systems, Institute of Information and Communication Technologies, Akad. G. Bonchev, bl. 2, Sofia 1113, Bulgaria

Abstract: In this paper, we consider the nonlinear matrix equation X + A*F(X)A = Q and we derive norm-wise non-local residual bounds for the accuracy of the solution obtained by an iterative algorithm. The residual bounds are derived using the method of Lyapunov majorants and the techniques of the fixed point principle. Two particular cases of the equation are considered in details and explicit expressions of the norm-wise non-local residual bounds are obtained as well. Numerical examples for the two, considered in the paper different cases of the nonlinear matrix function F(X) are provided to demonstrate the efficiency of the bounds proposed.

Keywords: perturbation analysis; residual bounds; nonlinear matrix equations; Lyapunov majorants; fixed point principle.

DOI: 10.1504/IJDS.2016.081370

International Journal of Data Science, 2016 Vol.1 No.4, pp.340 - 352

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 06 Jan 2017 *

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