Year: 2001
Author: Song-Bai Sheng, Hui-fu Xu
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 6 : pp. 583–590
Abstract
This paper presents an analysis of the generalized Newton method, approximate Newton methods, and splitting methods for solving nonsmooth equations from Picard iteration viewpoint. It is proved that the radius of the weak Jacobian (RGJ) of Picard iteration function is equal to its least Lipschitz constant. Linear convergence or superlinear convergence results can be obtained provided that RGJ of the Picard iteration function at a solution point is less than one or equal to zero. As for applications, it is pointed out that the approximate Newton methods, the generalized Newton method for piecewise $C^1$ problems and splitting methods can be explained uniformly with the same viewpoint.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-9010
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 6 : pp. 583–590
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Nonsmooth equations Picard iteration Weak Jacobian Convergence.