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