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Numerical Algorithms

, Volume 39, Issue 4, pp 415–435 | Cite as

A higher order family for the simultaneous inclusion of multiple zeros of polynomials

  • Miodrag S. Petković
  • Dušan M. Milošević
Article

Abstract

Starting from a suitable fixed point relation, a new family of iterative methods for the simultaneous inclusion of multiple complex zeros in circular complex arithmetic is constructed. The order of convergence of the basic family is four. Using Newton’s and Halley’s corrections, we obtain families with improved convergence. Faster convergence of accelerated methods is attained with only few additional numerical operations, which provides a high computational efficiency of these methods. Convergence analysis of the presented methods and numerical results are given.

Keywords

zeros of polynomials inclusion of zeros simultaneous methods convergence rate circular arithmetic 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Faculty of Electronic EngineeringUniversity of NišNišSerbia and Montenegro

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