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.
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An earlier version was presented at the Joint National Meeting of TIMS and ORSA, Las Vegas, May 7–9, 1990. Financial support from Økonomisk Forskningsfond, Bodø, Norway, is gratefully acknowledged. The author thanks an anonymous referee for helpful comments and suggestions.
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Thorlund-Petersen, L. Global convergence of Newton’s method on an interval. Math Meth Oper Res 59, 91–110 (2004). https://doi.org/10.1007/s001860300304
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DOI: https://doi.org/10.1007/s001860300304