Approximation of zeros of nonlinear real functions using a variant of the false position method based on quadratic polynomials

Castillo, Y.; Correa, S.; Ipanaqué, R.; Iman, C.; Farfán, J.

Indian Journal of Mathematics

Approximation of zeros of nonlinear real functions using a variant of the false position method based on quadratic polynomials

Author(s): Y. Castillo Y. Castillo Department of Mathematics,
National University of Piura,
Piura, Peru. ycastillom@egresados.unp.edu.pe , S. Correa S. Correa Department of Mathematics,
National University of Piura,
Piura, Peru. scorreae@.unp.edu.pe , R. Ipanaqué R. Ipanaqué Department of Mathematics,
National University of Piura,
Piura, Peru. ripanaquec@.unp.edu.pe , C. Iman C. Iman Faculty of Economics and Business Sciences,
University of Piura,
Piura, Peru. carlos.iman@.udep.edu.pe , J. Farfán J. Farfán Faculty of Economics and Business Sciences,
University of Piura,
Piura, Peru. javier.farfan@.udep.edu.pe

Vol. 67, No. 1 (2025) • pp. 1–23

Published 27-04-2026 Article History Received 01-08-2025 Revised 12-01-2026 Published 27-04-2026

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Abstract

We present a quadratic variant of the classical False Position Method (VQFPM) for approximating the zeros of nonlinear real functions. The method is based on second-degree Lagrange interpolation using three dynamic points within each iteration interval, which significantly improves the convergence rate without requiring derivatives. We establish the theoretical foundations of the method and derive rigorous bounds for its convergence error. Through numerical experiments implemented in the open-source software Maxima, we demonstrate that VQFPM achieves high precision with fewer iterations than traditional methods, including Newton and Secant. These results highlight VQFPM as a robust and efficient alternative for derivative-free root finding.

Keywords

Method, variant, false position, quadratic polynomials.

2020 Mathematics Subject Classification

65H05, 65D05

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Allahabad Mathematical Society

Approximation of zeros of nonlinear real functions using a variant of the false position method based on quadratic polynomials

Abstract

Keywords

2020 Mathematics Subject Classification

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