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Zbl 0886.65010
Barry, D.A.; Culligan-Hensley, P.J.; Barry, S.J.
Real values of the $W$-function. (English)
[J] ACM Trans. Math. Softw. 21, No.2, 161-171 (1995). ISSN 0098-3500

Summary: 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 $(|W|<1)$ errors of $O(10^{-4})$. 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.

MSC 2000:: *65D20 Computation of special functions
33B10 Elementary functions

Keywords: $W$-function; algorithm; iteration scheme

Citations: Zbl 0886.65011

Cited in: Zbl 0886.65011

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