Re: faster Interpolation?

• To: mathgroup at smc.vnet.net
• Subject: [mg58868] Re: faster Interpolation?
• From: "Mariusz Jankowski" <mjankowski at usm.maine.edu>
• Date: Thu, 21 Jul 2005 15:46:01 -0400 (EDT)
• Organization: University of Southern Maine
• References: <dbniuf\$hoj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Alessandro, the fastest approach is to (1) upsample your data and (2)
convolve.

(1) here I double the length of my data by inserting zeros

L = Length[data];
nL = 2 * Length[data];
zero = Table[0., {nL}];
zero[[ Range[1,nL,2] ]] = data;

(2) convolve

ListConvolve[ {0.5, 1., 0.5}, zero, 2, 0.]

However, if your data is length L, your result will be length 2L, then you
need a total of 24*L bytes of memory to do the job. Clearly, you will not be
able to work with data of size 10^9 samples (on 32-bit systems)!

Bye, Mariusz

>>> Alessandro Strumia<astrumia at mail.df.unipi.it> 07/21/05 3:30 AM >>>
hello,

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.

Thank you very much,
Alessandro Strumia

```

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