Re: Re: InverseFunction[]
- To: mathgroup at smc.vnet.net
- Subject: [mg42187] Re: [mg42160] Re: InverseFunction[]
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Sat, 21 Jun 2003 20:57:05 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <bbt23g$nj3$1@smc.vnet.net> <bc1jh1$bjp$1@smc.vnet.net> <200306110749.DAA02507@smc.vnet.net> <bc7pet$6f0$1@smc.vnet.net> <paul-000944.15584413062003@news.uwa.edu.au> <bcjv91$hv3$1@smc.vnet.net> <200306210649.CAA13213@smc.vnet.net>
- Reply-to: murray at math.umass.edu
- Sender: owner-wri-mathgroup at wolfram.com
Yes, you're correct: I did a copy-and-paste from the wrong line in the Help Browser window. Indeed: ProductLog uses highorder Newton's method starting from rational approximations and asymptotic expansions. Paul Abbott wrote: > In article <bcjv91$hv3$1 at smc.vnet.net>, > Murray Eisenberg <murray at math.umass.edu> wrote: > > >>Well, to take the example of the function you pose for comparison, Sin: >> The section "Some Notes on Internal Implementation" in the Mathematica >>Book's "Mathematica Reference Guide", says: >> >> Exponential and trigonometric functions use Taylor series, >> stable recursion by argument doubling, and functional relations. >> >>But I'm guilty of not scrolling down far enough on that same page to >>have discovered: >> >> PolyLog uses Euler-Maclaurin summation, expansions in terms >> of incomplete gamma functions and numerical quadrature. > > > PolyLog not ProductLog? > > ProductLog uses high-order Newton's method starting from rational > approximations and asymptotic expansions. > > >>That's the sort of thing I was looking for and somehow had previously >>overlooked! > > > So you were only interested in how Mathematica computes a function > numerically? This was not clear from your original question: > > >>But what is the definition of the function as Mathematica knows it? > > > To me the definition of a function is not how it is computed numerically. > > Cheers, > Paul > -- Reply to "REPLY TO" address and NOT to the "FROM" address!! Otherwise I will never see your reply!!!!!!!!!!!!!!!!!!!!!! Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
- References:
- Re: InverseFunction[]
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Re: InverseFunction[]
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Re: InverseFunction[]