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Local convergence of inexact Newton methods. (English) Zbl 0566.65037
Let D m and F:D m be a mapping. The author studies the approximate solution of the equation F(x)=0 by means of the iterative method for n=0,1,2,····: (*) x n+1 :=x n +s n m with s n from F ' (x n )s n =-F(x n )+r n for some sequence {r n }R m . He gives an affine invariant condition involving r n which ensures the local convergence of (*) to a solution of F(x)=0. Moreover he deduces a radius of convergence result for (*) which is shown to be sharp for both Newton’s method and the general difference Newton-like method. The results are applied to the latter two methods and the general Newton-like method in which the iterates are perturbed by the presense of rounding errors. No numerical example.
Reviewer: B.Döring

MSC:
65H10Systems of nonlinear equations (numerical methods)