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

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.