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author | zimmerma <zimmerma@280ebfd0-de03-0410-8827-d642c229c3f4> | 2016-06-03 12:26:21 +0000 |
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committer | zimmerma <zimmerma@280ebfd0-de03-0410-8827-d642c229c3f4> | 2016-06-03 12:26:21 +0000 |
commit | 5c58d718ae6097022e9581fe921b513afff1ab81 (patch) | |
tree | ce2419ac4ed8ac07fab2dbb6d08d161647d49b05 /TODO | |
parent | 68aa9767168cbfdef2f6b8f28cd7b1489b26d369 (diff) | |
download | mpfr-5c58d718ae6097022e9581fe921b513afff1ab81.tar.gz |
added reference for Lambert W function
git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@10417 280ebfd0-de03-0410-8827-d642c229c3f4
Diffstat (limited to 'TODO')
-rw-r--r-- | TODO | 7 |
1 files changed, 7 insertions, 0 deletions
@@ -234,6 +234,13 @@ Table of contents: + Lambert W Functions, W(x) are defined to be solutions of the equation: W(x) \exp(W(x)) = x. This function has multiple branches for x < 0 (2 funcs W0(x) and Wm1(x)) + From Fredrik Johansson: + See https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf, in particular + formulas 5.2 and 5.3 for the error bound: one first computes an + approximation w, and then evaluates the residual w e^w - x. There is an + expression for the error in terms of the residual and the derivative W'(t), + where the derivative can be bounded by piecewise simple functions, + something like min(1, 1/t) when t >= 0. + Trigamma Function psi'(x). and Polygamma Function: psi^{(m)}(x) for m >= 0, x > 0. - functions from ISO/IEC 24747:2009 (Extensions to the C Library, |