       Fast Integration of a product of 2 interpolating functions

• To: mathgroup at smc.vnet.net
• Subject: [mg26542] Fast Integration of a product of 2 interpolating functions
• From: Sebastien.deMentendeHorne at electrabel.com
• Date: Fri, 5 Jan 2001 00:33:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I'm facing the following problem:

f[x,y] and g[y,z] are two InterpolatingFunction (called IF)
f = FunctionInterpolation[Cos[x + y] + y^2, {x, -1., 1}, {y, -1.,
1}];
g = FunctionInterpolation[Exp[y] + z/(y + 2), {y, -1., 1}, {z, -1.,
1}];

I need to compute a numerical value for
Integrate[f[x,y] g[y,z], {y,-1,1}]
at a lot of points {x,z}.

The integration of an IF with Integrate is much faster than with NIntegrate.
However the product of 2 IFs is not an IF and hence, the integration with
Integrate is painfull.
Moreover, I can't create an IF h[x,y,z]=f[x,y] g[y,z] because of the memory
it will take.

Any idea to increase the speed of the integration in this case?

And a last question, with the function f and g defined above, why :
ByteCount[f]	=	2256
ByteCount[g]	=	2256
ByteCount[f g]	=	11608
IMHO, ByteCount[f g] should give something like 2256 + 2256 + small overhead
for Times[,]

Thanks

Sebastien de Menten de Horne      |    ELECTRABEL
Tel:  ++32 10 48 51 76            |    R&D Energy Markets,
Fax:  ++32 10 48 51 09            |    Traverse d'Esope, 6
Gsm:  ++32 478 789 444            |    B-1348 Louvain-la-Neuve, BELGIUM

```

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