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

TL;DR

This paper presents a novel numerical approach for approximating the Lambert W function on real numbers, using quadratic approximation and iterative refinement, applicable to both branches without restrictive assumptions.

Contribution

It introduces a new quadratic approximation-based numerical method for the Lambert W function that works for all real inputs and both branches.

Findings

Method achieves high accuracy in approximations.

Applicable to both positive and negative inputs.

Demonstrated effectiveness through examples and software.

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.