Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 2 : pp. 231–242
Abstract
Inexact Newton methods are constructed by combining Newton's method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton's method, we obtain a different Newton-Kantorovich theorem about Newton's method. When the iterative method for solving the Newton equations is specified to be the splitting method, we get two estimates about the iteration steps for the special inexact Newton methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8688
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 2 : pp. 231–242
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Banach space Systems of nonlinear equations Newton's method The splitting method Inexact Newton methods.