TY  - JOUR
T1  - Approximation of zeros of nonlinear real functions using a variant of the false position method based on quadratic polynomials
AU  - Castillo, Y.  
AU  - Correa,  S.
AU  - Ipanaqué, R.  
AU  - AIman, C.
AU  - Farfán, J.
JO  - Indian Journal of Mathematics
VL  - 67
IS  - 1
SP  - 1
EP  - 23
PY  - 2025
DA  - 2026/04/27
SN  - 0019-5324
KW  - Method, variant
KW  - false position
KW  - quadratic polynomials
KW  - Signed and weighted graphs.
AB  - 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.
ER  -