The Gauss-Newton Methods via Conjugate Gradient Path without Line Search Technique for Solving Nonlinear Systems. (2nd January 2017)

• Record Type: Journal Article
• Authors: Wang, Jueyu; Zhu, Detong
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 1(2017)
• Page Start: 110
• Page End: 137
• Publication Date: 2017-01-02
• Subjects: Conjugate gradient path -- Gauss-Newton method -- global convergence -- nonlinear systems; 65K05 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1232729
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we propose the Gauss-Newton methods via conjugate gradient path for solving nonlinear systems. By constructing and solving a linearized model of the nonlinear systems, we obtain the iterative direction by employing the conjugate gradient path. In successive iterations, the approximate Jacobian of the nonlinear systems is updated by a Broyden formula to construct the conjugate path. The global convergence and local superlinear convergence rate of the proposed algorithms are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithms.