On Newton-type methods for multiple roots 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:
2009

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Abstract

We introduce two families of Newton-type methods for multiple roots with cubic convergence. A further Newton-type method for multiple roots with cubic convergence is presented that is related to quadrature. We also provide numerical tests that show that these new methods are competitive to other known methods for multiple roots.