A modified three-point Secant method with improved rate and characteristics of convergence
Abstract: This paper presents a modification of Secant method for finding roots of equations that uses three points for iteration instead of just two. The development of the mathematical formula to be used in the iteration process is provided together with the proof of the rate of convergence which is 1.84 and is the same as the rate of convergence of Mueller's method of root finding. In fact the method is yet a discovery of a family member of Mueller's method that has linear form. Application examples are given where it is demonstrated that for equations involving ill-conditioned cases, the proposed method has better convergence characteristics compared to Newton and Secant methods.
Keywords: Root finding, Secant method, Mueller’s method, Newton method, rate of numerical method.
How to cite this article:
Ababu T. Tiruneh, Tesfamariam Y. Debessai, Gabriel C. Bwembya and Stanley J. Nkambule, A modified three-point Secant method with improved rate and characteristics of convergence, International Journal of Advances in Mathematics, Volume 2019, Number 4, Pages 69-83, 2019.