Real values of the W-function

Authors:
D. A. Barry;P. J. Culligan-Hensley;S. J. Barry
Affiliations:
Univ. of Western Australia, Nedlands, W.A., Australia;Univ. of Western Australia, Nedlands, W.A., Australia;Griffith Univ., Nathan, Queensland, Australia
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1995

Citing 3
Cited 4

Algorithm 743: WAPR--a Fortran routine for calculating real values of the W-function

ACM Transactions on Mathematical Software (TOMS)
Solution of the transcendental equation wew = x

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Algorithm 743: WAPR--a Fortran routine for calculating real values of the W-function

ACM Transactions on Mathematical Software (TOMS)
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Abstract

Approximations for real values of W(x), where W is defined by solutions of W exp(W) = x, are presented. All of the approximations have maximum absolute (|W|1) or relative (|W|O(10−4). With these approximations an efficient algorithm, consisting of a single iteration of a rapidly converging iteration scheme, gives estimates of W(x) accurate to at least 16 significant digits (15 digits if double precision is used). The Fortran code resulting from the algorithm is written to account for the different floating-point-number mantissa lengths on different computers, so that W(x) is computed to the floating-point precision available on the host machine.