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Re: faster Interpolation?

• To: mathgroup at smc.vnet.net
• Subject: [mg58886] Re: faster Interpolation?
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Fri, 22 Jul 2005 01:58:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On 7/21/05 at 3:08 AM, astrumia at mail.df.unipi.it (Alessandro
Strumia) wrote:

>I need to compute a linear interpolation of a single-parameter
>function defined on an equally-spaced grid, and I do not need its
>derivatives.

>The ListInterpolation function of Mathematica can do this and much
>more, but it is not fast enough for my purposes: it takes almost
>10^-3 Second on my computer, and I need to compute the function in
>about 10^9 points. The total running time would be about one month:
>too slow!

>So I wonder if there is a faster alternative.

One simple way to improve speed would be to only interpolate points around the values of interest at the momement. That is the interpolation algorithms used perform a local interpolation to the order specified. For a linear interpolation, this means only the two points on either side of the value of interest. So, by asking Mathematica to interpolate all 10^9 points you are doing far more computation than needed to get the interpolated result for a handful of values.
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