Recursive approximations of both real branches of the Lambert W function via elementary functions.
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Monotone recursive approximations with explicit starting values and simple, uniform error estimates.
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Recursive approximations with quadratic convergence rate.
Abstract
Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert function. The function, also occurring frequently in many branches of science, is a non-elementary but now standard mathematical function implemented in all major technical computing systems. In this work, we analyze an efficient logarithmic recursion with quadratic convergence rate to approximate its two real branches, and . We propose suitable starting values that ensure monotone convergence on the whole domain of definition of both branches. Then, we provide a priori, simple, explicit and uniform estimates on the convergence speed, which enable guaranteed, high-precision approximations of and at any point.
Keywords
Lambert W function
Explicit estimates
Recursive approximations
Data Availability
No data was used for the research described in the article.
The project “Application-domain specific highly reliable IT solutions” has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the Thematic Excellence Programme TKP2020-NKA-06 (National Challenges Subprogramme) funding scheme.