Global approximations to the principal real-valued branch of the Lambert W-function

被引:34
作者
Boyd, JP [1 ]
机构
[1] Dept Atmospher Ocean & Space Sci, Ann Arbor, MI 48109 USA
基金
美国国家科学基金会;
关键词
Lambert W-function; global approximations; rational Chebyshev function series;
D O I
10.1016/S0893-9659(98)00097-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
W(z) is defined implicitly as the root of W exp(W) = z. It is shown that a simple analytic approximation has a relative error of less than 5% over the whole domain z is an element of [- exp(-1), infinity] of the principle branch-sufficiently accurate so that four Newton iterations refine this approximation to a relative error smaller than 1.E-12. As a second form of global approximation, the W-function is expanded as a series of rational Chebyshev functions TBj in a shifted, logarithmic coordinate with an error that decreases exponentially fast with the series truncation. (C) 1998 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:27 / 31
页数:5
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