Comparative Testing of Five Numerical Methods for Finding Roots of Polynomials

Abstract

This paper summarizes the results of comparative testing of (1) Wilf's global bisection method, (2) the Laguerre method, (3) the companion matrix eigenvalue method, (4) the companion matrix eigenvalue method with balancing, and (5) the Jenkens-Traub method, all of which are methods for finding the zeros of polynomials. The test set of polynomials used are those suggested by [5]. The methods were compared on each test polynomials on the basis of the accuracy of the computed roots and the CPU time required to numerically compute all roots.