• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.323-340
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• 1997

In this study we prove the mesh-independence principle via Steffensen's method. This principle asserts that when Steffensen's method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation then the behavior of th discretized process is asymptoti-cally the same as that for the original iteration. Local and semilo-cal convergencve results as well as an error analysis for Steffensen's method are also provided.

• 대한수학회지
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• 제54권1호
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• pp.17-33
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• 2017

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as [1-13], [21, 22]. Numerical examples are provided to illustrate the theoretical results.