Conventional numerical methods for finding multiple roots of polynomials are inaccurate. The accuracy is unsatisfactory because the derivatives of the polynomial in the intermediate steps of the associated root-finding procedures are eliminated. Engineering applications require that this problem be
Multiple root-finding methods
β Scribed by M. Vander Stracten; H. Van de Vel
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 834 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0377-0427
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π SIMILAR VOLUMES
In this paper, an iteration method without derivatives for multiple roots is proposed. This method proved to be quadratically convergent. Its efficiency and accuracy are illustrated by numerical experiments.
For an equation f (x) = 0 having a multiple root of multiplicity m > 1 unknown, we propose a transformation which converts the multiple root to a simple root of H (x) = 0. The transformed function H (x) of f (x) with a small > 0 has appropriate properties in applying a derivative free iterative meth
a b s t r a c t Two accelerating generators that produce iterative root-finding methods of arbitrary order of convergence are presented. Primary attention is paid to algorithms for finding multiple roots of nonlinear functions and, in particular, of algebraic polynomials. First, two classes of algor