Geodesic
FP//LINSPACE evaluation of real Lambert W-function~$W_0$
Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 111-116

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In the paper, we construct FP//LINSPACE algorithmic analog of real Lambert W-function $W_0(x)$ on segment $[-(re)^{-1},(re)^{-1}]$ of FP//LINSPACE algorithmic real numbers, where $r$ is a rational number, $r>4/3$ (any such rational number is suitable). To construct algorithmic analog of real Lambert W-function $W_0(x)$, we consider algorithm WLE for the evaluation of dyadic rational approximations of the function on segment $[-(re)^{-1},(re)^{-1}]$ on Turing machine using polynomial time and linear space. Algorithm WLE is based on the Taylor series expansion of the function; it is shown that the Taylor series of real Lambert W-function $W_0(x)$ on segment $[-(re)^{-1},(re)^{-1}]$ converges linearly. This fact is used in the algorithm.
Keywords: real Lambert W-function $W_0$, algorithmic real functions, Turing machine, polynomial time complexity, linear space complexity. 
@article{PDM_2014_3_a10,
     author = {M. A. Staritzyn and S. V. Yakhontov},
     title = {FP//LINSPACE evaluation of real {Lambert} {W-function~}$W_0$},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {111--116},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_3_a10/}
}
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M. A. Staritzyn; S. V. Yakhontov. FP//LINSPACE evaluation of real Lambert W-function~$W_0$. Prikladnaâ diskretnaâ matematika, no. 3 (2014), pp. 111-116. http://geodesic.mathdoc.fr/item/PDM_2014_3_a10/