Volume 25, Issue 2
On Semilocal Convergence of Inexact Newton Methods

Xueping Guo

DOI:

J. Comp. Math., 25 (2007), pp. 231-242

Published online: 2007-04

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  • 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.

  • Keywords

Banach space Systems of nonlinear equations Newton's method The splitting method Inexact Newton methods

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COPYRIGHT: © Global Science Press

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@Article{JCM-25-231, author = {}, title = {On Semilocal Convergence of Inexact Newton Methods}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {2}, pages = {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.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8688.html} }
TY - JOUR T1 - On Semilocal Convergence of Inexact Newton Methods JO - Journal of Computational Mathematics VL - 2 SP - 231 EP - 242 PY - 2007 DA - 2007/04 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8688.html KW - Banach space KW - Systems of nonlinear equations KW - Newton's method KW - The splitting method KW - Inexact Newton methods AB - 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.
Xueping Guo. (1970). On Semilocal Convergence of Inexact Newton Methods. Journal of Computational Mathematics. 25 (2). 231-242. doi:
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