Derivation and Application of the Graeffe’s Roots Squaring Algorithm for the Second Order Polynomial of the form \(f(x)=0\)
O. D. Ogwumu *
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
I. K. Andrew
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
E. O. Ogbaji
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
M. O. Ogofotha
Department of Mathematics and Statistics, Federal University Wukari, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The research is concerned with the derivation of the Graeffe’s root squaring Algorithm for the solution the polynomials of the form \(f(x)=0\) . Thereafter, the algorithm was in validated by applying it to some range of problems in literatures reviewed. The outcome of the comparison of the roots generated by the Graeffe’s Root Finding Algorithm showed that our scheme gave a better approximation closed to the exact solution after the fourth iteration. Thus, the proposed scheme in this research can be said to be another better suitable numerical approach for solution of the polynomials that their exact solutions are difficult to arrive at. The procedures for the scheme derivation can be easily followed for the solution of higher order polynomials.
Keywords: Animal Cytotaxonomy, Graeffe’s Scheme, Crustacean Chromosomes, numerical approach, Crab Cytology, root-finding-algorithm, second order polynomial, exact solution