A modified Newton method for rootfinding with cubic convergence

Authors:
H. H. H. Homeier
Affiliations:
Institut für Physikalische und Theoretische Chemie, Universität Regensburg, 93040 Regenburg, Germany and science + computing ag, Ingolstädter Str. 22, 80807 München, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

We consider a modification of the Newton method for finding a zero of a univariate function. The case of multiple roots is not treated. It is proven that the modification converges cubically. Per iteration it requires one evaluation of the function and two evaluations of its derivative. Thus, the modification is suitable if the calculation of the derivative has a similar or lower cost than that of the function itself. Classes of such functions are sketched and a numerical example is given.