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Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms

Author

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  • Chaman Lal Sabharwal

    (Computer Science Department, Missouri University of Science and Technology, Rolla, MO 65409, USA)

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.

Suggested Citation

  • Chaman Lal Sabharwal, 2019. "Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1118-:d:287709
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    Cited by:

    1. S. Sapna & Biju R. Mohan, 2024. "Comparative Analysis of Root Finding Algorithms for Implied Volatility Estimation of Ethereum Options," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 515-550, July.

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