Rates of Convergence for a Class of Iterative Procedures

In this paper we shall give an extension of Ostrowski's point of attraction theorem to multistep iterative procedures for finding a zero of a nonlinear function defined on Rn. We shall also obtain a rate of convergence statement in terms of the spectral radius of certain matrices. These results...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 8; no. 1; pp. 127 - 134
Main Author Voigt, Robert G.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.03.1971
Subjects
Logical givens
Mathematical procedures
Mathematical theorems
Newtons method
Perceptron convergence procedure
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Summary:In this paper we shall give an extension of Ostrowski's point of attraction theorem to multistep iterative procedures for finding a zero of a nonlinear function defined on Rn. We shall also obtain a rate of convergence statement in terms of the spectral radius of certain matrices. These results will then be applied to a class of procedures obtained by composing one-dimensional iterative methods with the Jacobi and successive-overrelaxation processes. The rate of convergence of these procedures will be shown to be independent of the rate of convergence of the one-dimensional methods.
ISSN:0036-1429
1095-7170
DOI:10.1137/0708016