Some Generalizations of the Chebyshev Method for Simultaneous Determination of All Roots of Polynomial Equations

TL;DR

This paper discusses generalized iterative methods with cubic convergence for simultaneously finding all roots of polynomial equations, assuming known root multiplicities, supported by numerical examples.

Contribution

It introduces new generalizations of the Chebyshev method for root-finding with proven cubic convergence rates.

Findings

Methods converge cubically to all roots

Numerical examples demonstrate effectiveness

Assumes known root multiplicities

Abstract

Iterative methods for the simultaneous determination of all roots of an equation are dis-cussed. The multiplicities of the roots are assumed to be known in advance. The methods are proved to have a cubical rate of convergence. Numerical examples are given.