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This paper presents a modification of Secant method for finding roots ofequations that uses three points for iteration instead of just two. Thedevelopment of the mathematical formula to be used in the iteration process isprovided together with the proof of the rate of convergence which is the sameas the rate of convergence of Muller method of root finding. Applicationexamples are given where it is demonstrated that for equations involving illconditioned cases, the proposed method has better convergence characteristicscompared to Newton and Secant methods.

A modified three-point Secant method with improved rate and characteristics of convergence