Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms

Chaman Lal Sabharwal
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Chaman Lal Sabharwal: Computer Science Department, Missouri University of Science and Technology, Rolla, MO 65409, USA

Mathematics, 2019, vol. 7, issue 11, 1-16

Abstract: Finding the roots of an equation is a fundamental problem in various fields, including numerical computing, social and physical sciences. Numerical techniques are used when an analytic solution is not available. There is not a single algorithm that works best for every function. We designed and implemented a new algorithm that is a dynamic blend of the bisection and regula falsi algorithms. The implementation results validate that the new algorithm outperforms both bisection and regula falsi algorithms. It is also observed that the new algorithm outperforms the secant algorithm and the Newton–Raphson algorithm because the new algorithm requires fewer computational iterations and is guaranteed to find a root. The theoretical and empirical evidence shows that the average computational complexity of the new algorithm is considerably less than that of the classical algorithms.

Keywords: bisection; regula falsi; Newton–Raphson; secant; blended algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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