The Exact Root Algorithm for Computing the Real Roots of an Nth Degree Polynomial

Adebile Adebile

doi:10.3844/jmssp.2010.226.232

Abstract

Problem statement: The need to find an efficient and reliable algorithm for computing the exact real roots of the steady-state polynomial encountered in the investigation of temperature profiles in biological tissues during Microwave heating and other similar cases as found in the literature gave rise to this study. Approach: The algorithm (simply called ERA-Exact Root Algorithm) adopted polynomial deflation technique and uses Newton-Raphson iterative procedure though with a modified termination rule. A general formula was specified for finding the initial approximation so as to overcome the limitation of local convergence which is inherent in Newton’s method. Results: A new algorithm for finding the real roots of an nth degree polynomial at a practically low computational cost was obtained. Conclusion/Recommendations: ERA is simple, flexible, easy to use and has clear benefits and preferences to a number of existing methods.

Highlights

The classical problem of solving an nth degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present-day computing as reported by Pan (1997).Jenkins-Traub algorithm, a three-stage method for computing the zeros of a polynomial in roughly increasing order of magnitude was presented by Jenkins and Traub (1970)
We present a new algorithm for finding the exact real roots of an nth degree polynomial at a practically low computational cost
This study presents a very efficient and reliable algorithm for computing the exact real roots of an nth degree polynomial which has the following benefits over the standard existing methods earlier mentioned:

Summary

Introduction

The classical problem of solving an nth degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present-day computing as reported by Pan (1997).Jenkins-Traub algorithm, a three-stage method for computing the zeros of a polynomial in roughly increasing order of magnitude was presented by Jenkins and Traub (1970). Jenkins-Traub algorithm, a three-stage method for computing the zeros of a polynomial in roughly increasing order of magnitude was presented by Jenkins and Traub (1970). Edelman and Murakami (1995) presented a good method for computing the zeros of a polynomial P(x).

Results

Conclusion