Re: RationalApproximation

• To: mathgroup at smc.vnet.net
• Subject: [mg55065] Re: RationalApproximation
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Fri, 11 Mar 2005 04:20:40 -0500 (EST)
• Organization: University of Washington
• References: <d0p7q0\$j44\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Scott,

One typical idea is to write a wrapper function which stores the values of
its arguments. Using one of the examples in the help for
RationalInterpolation,

RationalInterpolation[Exp[x],{x,2,4},{x,0,2}]

we can modify as follows:

pts={};
g[x_?NumericQ]:=(pts={pts,x};Exp[x])
RationalInterpolation[g[x],{x,2,4},{x,0,2}]
Flatten[pts]

The variable pts stores the set of values chosen as a nested list for
efficiency reasons. The values you want are obtained by flattening pts.

Carl Woll

"Scott Guthery" <sguthery at mobile-mind.com> wrote in message
news:d0p7q0\$j44\$1 at smc.vnet.net...
> 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
> Subject: [mg55065] 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
>
>
>

```

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