The Exact Root Algorithm for Computing the Real Roots of an Nth Degree Polynomial
E. A. Adebile and V. I. Idoko
DOI : 10.3844/jmssp.2010.226.232
Journal of Mathematics and Statistics
Volume 6, 2010
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.
© 2010 E. A. Adebile and V. I. Idoko. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.