Section 6.11

02-07-2008, 03:00 AM

Love the book!

Section 6.11 talks about inverting the function
y = x*log(x).

It doesn't mention the Lambert W function, which inverts
y = x*exp(x). Thus W(x)*exp(W(x)) = x.

The y(x) of equation 6.11.1 would then be exp(W(x)).

There are a load of references (the canonical one would be
Corless 1996).

HTH, Robinh

10-14-2008, 10:30 AM
Indeed, there is no mention of the Lambert W function anywhere in the text. :)

Note, for the unwary, that the precise function returned by the NR routine is exp(W-1(x)), i.e., the "other" real branch of Lambert W and not the "principal branch", W0(x).

Should anybody contemplate writing an implementation of Lambert W, Halley's method is very much fine for the purpose. as to good starting values, a good one was proposed by S. Winitzki (Winitzki, S. “Uniform Approximations for Transcendental Functions.” In Computational Science and Its Applications – ICCSA 2003).

Hope this information is useful. i would love to see the Lambert function added to NR's later editions.

Jan M. (^_^)

P.S. "You last visited: 12-02-2004" - has it been that long?