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MathGroup Archive 2005

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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


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