(28/48/50) Lambert W Function
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03-22-2023, 07:30 PM
Post: #6
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RE: (28/48/50) Lambert W Function
(03-21-2023 05:15 PM)Albert Chan Wrote: I am unfamilar with RPL, can you post actual formula for W(a) guess, and the iteration formula? Many thanks for the mpmath github reference, that solved my branch problem! Updated program will follow soon. Here are the formulas that you requested: Formula for global approximation of W(z) for branch 0. From "New approximations to the principal real-valued branch of the Lambert W-function", by Iacono and Boyd. -1 + a*ln((1 + b*y)/(1 + c*ln(1+y)) where y = sqrt(1+e*x) c = (e^(1/a) - 1 - sqrt(2)/a)/(1 - e^(1/a)*ln(2)) b = sqrt(2)/a + c With 'a' determined empirically to be 2.036, final formula is: -1 + 2.036*ln((1 + 1.14956131*y)/(1 + 0.4549574*ln(1 + y)) Recurrence from same paper, also from "Guaranteed- and high-precision evaluation of the Lambert W function" by Lajos Lóczi. B'(x) = (B(x)/(1 + B(x))*(1 + ln(x/B(x)) where B(x) is current estimate B'(x) is new estimate |
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