Ideas? Suggestions?I've googled already

Here's a link that may help:http://www.mathworks.com/access/helpdes ... erp15.html

Thanks... I should precise the question. The function to approximate is a black box, therefore the real problem ishow to choose the (say, interpolation) points. Or maybe just OLS, but, again, which points one has to choose.

You can use a development with Tchebychev polynomials to minimize the error. they have a better behaviour than lagrange.

Do you want to approximate over an interval? Or over R^n?

It was over whole R^n, but out of big interval, there is no big difference (the parameters over whichthe integration should have been done are sort of normal).Actually, I've found another way: as Shadoks (the French cartoon caracters) say 'If there is no solution, then there is no problem!'... ( S'il n'y a pas de solution c'est qu'il n'y a pas de problème!)

Hi pjakubenas,Maybe it would be helpful to map R^2 onto the 2-sphere using stereographic projection and then use standard spherical harmonics, which form a complete orthogonal set. Je ne sais pas si cela marcherait ou pas.--------------

Moi non plus...I'll test it when the occasion arises...

OK. What is the behavior of your function at infinity? In particular, how much variation exists as infinity is approached in different directions in the R^2 = (x,y) plane? If your function goes to zero at infinity, polynomial approximations in (x,y) may not be so useful. Also, there are now multivariate Pade approximation methods that might be helpful. You can get references on Google Scholar.I also found a reference to this article which has an unusual approach. Unfortunately you have to subscribe to actually read the article:---------------Two-Series Approach to Partial Differential Approximants: Three-Dimensional Ising ModelsM. J. George and J. J. Rehr Department of Physics, University of Washington, Seattle, Washington 98195Received 1 August 1984A two-series approach to partial differential approximant analysis of power series is presented. Instead of double series, f(x,y)=SUM [cijxiyj], our approach uses two one-variable series in x, f and [partial] f / [partial] y, and has the efficiency and stability of one-variable methods. 21-term high-temperature series are analyzed for the susceptibility and correlation length squared for double-Gaussian Ising models on the bcc lattice. Critical exponents are gamma =1.2378(6), 2 nu =1.2623(6), and eta =0.0375(5); correction-to-scaling exponents are theta chi =0.52(3) and theta xi 2=0.49(4); and the subdominant critical amplitude ratio is a xi / a chi =0.83(5).©1984 The American Physical SocietyURL: http://link.aps.org/abstract/PRL/v53/p2 ... ----------