Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2018, Article ID 3291867, 8 pages
https://doi.org/10.1155/2018/3291867
Research Article

Condition Numbers of the Nonlinear Matrix Equation

Department of Mathematics, Pusan National University, Busan 46241, Republic of Korea

Correspondence should be addressed to Chacha Stephen Chacha; moc.oohay@nehpetshchc

Received 25 April 2018; Accepted 19 July 2018; Published 1 August 2018

Academic Editor: Henryk Hudzik

Copyright © 2018 Chacha Stephen Chacha and Syed Muhammad Raza Shah Naqvi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We explore the condition numbers of the nonlinear matrix equation . Explicit expressions for the normwise, mixed, and componentwise condition numbers are derived. The upper bounds for the mixed and componentwise condition numbers are obtained. The numerical result favors the fact that our estimations are fairly sharp. Also, the relative upper perturbation bounds give satisfactory results for small perturbations in the input data.