Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642855 | Journal of Computational and Applied Mathematics | 2007 | 13 Pages |
Abstract
A one parameter family of iteration functions for finding simple and multiple zeros of analytic functions is derived. The family includes, as a special case, Traub's quartic square root method and, as limiting cases, the Kiss method of order 4, the Halley and the Newton methods. All the methods of the family are locally quartically convergent for a simple or multiple zero with known multiplicity. The asymptotic error constants for the methods of the family are given. The decreasing ratio at infinity of iteration functions is discussed. The optimum parameter of the family for polynomials is given.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Naoki Osada,