Asymptotic error constants of cubically convergent zero finding methods

Authors:
Naoki Osada
Affiliations:
Tokyo Woman's Christian University, Zempukuji, Suginamiku, Tokyo, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

The Laguerre family of iteration functions for finding multiple zeros is considered. This family is algebraically equivalent to the multiple zero counterpart of Hansen-Patrick family. The asymptotic error constant for the Laguerre family is given. The magnitude of asymptotic error constants for cubically convergent iteration functions for finding multiple real zeros of real functions are compared. Numerical examples are given.