A modified three-point Secant method with improved rate and characteristics of convergence
Incremental improvement for numerical root-finding in ill-conditioned cases.
The paper proposes a modified Secant method using three points instead of two, achieving a convergence rate equal to Muller's method. It demonstrates improved convergence for ill-conditioned equations compared to Newton and Secant methods.
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 the same as the rate of convergence of Muller method of root finding. 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.