Improved Iterative Methods for Solving High Order Polynomial Equations

Abstract

Many calculations in engineering and scientific computation can summarized to the problem of solving a polynomial equation. Based on Sturm theorem, an adaptive algorithm for real root isolation is shown. This algorithm will firstly find the isolate interval for all the real roots rapidly. And then approximate the real roots by subdividing the isolate intervals and extracting subintervals each of which contains one real root. This method overcomes all the shortcomings of dichotomy method and iterative method. It doesn’t need to compute derivative values, no need to worry about the initial points, and could find all the real roots out parallelly.