Numerical Approximation of Lambert W Function For Real Values By Unique Method of Quadratic Approximation

Abstract

This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies are proposed for positive inputs, and the method is extended to handle negative inputs within a defined range. Unlike standard methods, this approach works for both branches without restrictive initial assumptions. Examples and software demonstrate the accuracy and flexibility of the method.