Research Article Open Access

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

E. A. Adebile and V. I. Idoko

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.

Journal of Mathematics and Statistics
Volume 6 No. 3, 2010, 226-232

DOI: https://doi.org/10.3844/jmssp.2010.226.232

Submitted On: 11 March 2010 Published On: 30 September 2010

How to Cite: Adebile, E. A. & Idoko, V. I. (2010). The Exact Root Algorithm for Computing the Real Roots of an Nth Degree Polynomial. Journal of Mathematics and Statistics, 6(3), 226-232. https://doi.org/10.3844/jmssp.2010.226.232

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Keywords

  • Algorithm
  • computational cost
  • nth degree polynomial
  • real roots