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Zbl 1142.65354
Guo, Xueping
On semilocal convergence of inexact Newton methods. (English)
[J] J. Comput. Math. 25, No. 2, 231-242 (2007). ISSN 0254-9409; ISSN 1991-7139/e

Summary: 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, the author establishes two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton's method, the author obtains 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, the author gets two estimates about the iteration steps for the special inexact Newton methods.

MSC 2000:: *65H10 Systems of nonlinear equations (numerical methods)

Keywords: systems of nonlinear equations; Newton's method; splitting method; inexact Newton methods; semilocal convergence; Newton-Kantorovich theorem

Cited in: Zbl 1259.65075 Zbl 1165.65354 Zbl pre05559068

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