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Global convergence of Newton’s method on an interval

Author

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  • Lars Thorlund-Petersen

Abstract

The solution of an equation f(x)=γ given by an increasing function f on an interval I and right-hand side γ, can be approximated by a sequence calculated according to Newton’s method. In this article, global convergence of the method is considered in the strong sense of convergence for any initial value in I and any feasible right-hand side. The class of functions for which the method converges globally is characterized. This class contains all increasing convex and increasing concave functions as well as sums of such functions on the given interval. The characterization is applied to Kepler’s equation and to calculation of the internal rate of return of an investment project. Copyright Springer-Verlag 2004

Suggested Citation

  • Lars Thorlund-Petersen, 2004. "Global convergence of Newton’s method on an interval," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 91-110, January.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:1:p:91-110
    DOI: 10.1007/s001860300304
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    Cited by:

    1. Regina S. Burachik & C. Yalçın Kaya & Shoham Sabach, 2012. "A Generalized Univariate Newton Method Motivated by Proximal Regularization," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 923-940, December.

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