Local convergence of difference Newton-like methods

Ypma, T. J.

doi:10.1090/S0025-5718-1983-0717700-4

Local convergence of difference Newton-like methods
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by T. J. Ypma PDF

Math. Comp. 41 (1983), 527-536 Request permission

Abstract:

Using affine invariant terms, we give a local convergence analysis of difference Newton-like methods for solving the nonlinear equation $F(x) = 0$. The convergence conditions are weaker than those standardly required for methods of this class. The technique and results are valid for all currently known difference Newton-like methods which require evaluation of all components of F at the same point. Radius of convergence and rate of convergence results for particular difference Newton-like methods may easily be derived from the results reported here.

References

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Numerical Solution of Systems of Nonlinear Algebraic Equations