Elsevier

Applied Mathematics Letters

Volume 74, December 2017, Pages 94-101
Applied Mathematics Letters

On a high-order one-parameter family for the simultaneous determination of polynomial roots

https://doi.org/10.1016/j.aml.2017.05.013Get rights and content
Under an Elsevier user license
open archive

Abstract

A new one-parameter family of simultaneous methods for the determination of all (simple or multiple) zeros of a polynomial is derived. The order of the basic family of simultaneous methods is four. Using suitable corrective approximations, the order of convergence of this family is increased even to six without any additional evaluations of the polynomial and its derivatives, which points to a high computational efficiency of the new family of root solvers. Comparison with the existing methods in regard to computational efficiency and numerical examples are also performed.

Keywords

Polynomial zeros
Parametric iterative methods
Simultaneous methods
Convergence analysis
Computational efficiency

Cited by (0)