On Iterative Algorithm and Perturbation Analysis for the Nonlinear Matrix Equation

作     者：Chacha Stephen Chacha Chacha Stephen Chacha

作者机构：Department of MathematicsPhysics and InformaticsMkwawa University College of EducationP.O.Box 2513IringaTanzania 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2022年第4卷第3期

页      面：1158-1174页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：The author thanks three anonymous reviewers for their valuable observations  suggestions  and quite useful constructive comments 

主　　题：Mixed condition number Componentwise condition number Iterative algorithm Perturbation analysis Exact line search 

摘      要：In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=*** expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix *** analysis for the derived condition numbers and the proposed algorithm are *** proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line *** condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.