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Error bounds for the modified Newton's method

Published online by Cambridge University Press:  17 April 2009

A.L. Andrew
A.L. Andrew
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria.
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Abstract

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A strengthened form of the Kantorovich convergence theorem for the modified Newton's method is proved. The result is compared with previously known results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 427 - 433
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Dennis, J.E. Jr., “On the Kantorovich hypothesis for Newton's method”, SIAM J. Numer. Anal. 6 (1969), 493–507.CrossRefGoogle Scholar
[2]Kantorovich, L.V. and Akilov, G.P., Functional analysis in normed spaces (translated by Brown, D.E.. International Series of Monographs in Pure and Applied Mathematics, 46. Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfurt, 1964).Google Scholar
[3]Ortega, J.M. and Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables (Academic Press, New York and London, 1970).Google Scholar
[4]Roberts, Sanford M., Shipman, Jerome S., Two-point boundary value problems: shooting methods (Modern Analytic and Computational Methods in Science and Mathematics, 31. American Elsevier, New York, 1972).Google Scholar