Re: RationalApproximation
- To: mathgroup at smc.vnet.net
- Subject: [mg55078] Re: RationalApproximation
- From: Peter Pein <petsie at arcor.de>
- Date: Fri, 11 Mar 2005 04:21:05 -0500 (EST)
- References: <A4628A7C27BF0D48847FD4AB8536731D4E5015@blinky.mobile-mind.com> <d0p82h$j59$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
DrBob wrote: > It's pretty clear those points aren't available, except (possibly) by solving for the zeroes of the error. > > Bobby > > On Wed, 9 Mar 2005 10:01:30 -0500, Scott Guthery <sguthery at mobile-mind.com> wrote: > > >>My bad. RationalInterpolation[]. The docs say: >> >>"There are two ways of using RationalInterpolation. If you just specify >>a range in the independent variable, then the set of values is chosen >>automatically in a way that ensures a reasonable approximation for the >>degree of approximation you have chosen." >> >>The question is what is the set of values was chosen automatically. >> >>Cheers, Scott >> >>-----Original Message----- >>From: DrBob [mailto:drbob at bigfoot.com] To: mathgroup at smc.vnet.net >>Sent: Wednesday, March 09, 2005 9:43 AM >>To: Scott Guthery; mathgroup at smc.vnet.net >>Subject: [mg55078] Re: RationalApproximation >> >>I find no such function in Help for version 5.1.1, and no match for it >>at WRI's documentation center. If searches like this always worked (but >>they don't), that would mean there is no such function. You may have to >>tell us what package the function comes from, before we can find any >>clues on it. >> >>The Calculus`Pade` package has EconomizedRationalApproximation and >>NumericalMath`Approximations` has a similar function called >>RationalInterpolation, but I see no sign that either of them "ends up >>using" any set of points at all. >> >>Bobby >> >>On Wed, 9 Mar 2005 06:34:28 -0500 (EST), Scott Guthery >><sguthery at mobile-mind.com> wrote: >> >> >>>Is there any way to get RationalApproximation n automatic mode to give >> >>you back the set of points that it ended up using? >> >>>Thanks for any insight. >>>Cheers, Scott >>> >>> >>> >>> >> >> >> >>-- >>DrBob at bigfoot.com >> >> It's just a guess, but seems reasonable: In[1]:= innerMost[lst_,dr_:0]:=lst[[Sequence@@Drop[Dimensions[lst],-dr]]]; tr=Trace[RationalInterpolation[Sin[x],{x,3,2},{x,0,\[Pi]}], NumericalMath`Approximations`Private`xx]; innerMost[innerMost[tr,1][[3]]] Out[3]= {0.0535236,0.460076,1.16424,1.97735,2.68152,3.08807} -- Peter Pein Berlin