In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the ...In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix equation.Comparative analysis for the derived condition numbers and the proposed algorithm are presented.The proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line searches.Componentwise condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.展开更多
In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent...In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent point sequence, then the limitpoint of the sequence is a critical point of the objective function.展开更多
文摘In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix equation.Comparative analysis for the derived condition numbers and the proposed algorithm are presented.The proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line searches.Componentwise condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.
文摘In this paper we discuss the convergence of the Broyden algorithms withoutconvexity and exact line search assumptions. We proved that if the objective function issuitably smooth and the algorithm produces a convergent point sequence, then the limitpoint of the sequence is a critical point of the objective function.
