A Comparative Study of Mitat-Root, Newton–Raphson, Regula Falsi, Bisection, and Fixed-Point Iteration for High-Degree Polynomial Root Finding

Abstract

Root finding for high-degree polynomials remains a fundamental numerical task in scientific computing and engineering. This paper
compares five iterative approaches—Mitat-Root (a curvature/circle-inspired third-order method), Newton–Raphson, Regula Falsi,
Bisection, and Fixed-Point iteration—on five polynomial equations of degree at least five. A unified experimental pipeline automatically
brackets real roots and evaluates each method in terms of convergence success, iteration count, computational time, and final residual. The
results confirm the expected robustness of bracketing methods and the high speed of derivative-based methods when safeguarded, while fixedpoint iteration is strongly dependent on the contraction property of ????(????). The study provides reproducible Python code and graphical
diagnostics.