I have a (nonlinear) function which takes as input 4 parameters and produces a real number as output. It is quite complex to compute the function value given a set of parameters (as it requires a very big summation).
I'd like to answer queries on this function efficiently so I was thinking of trying to use some interpolation methods. I have used Chebyshev polynomials to interpolate univariate functions, but I haven't been able to find (or understand) anything on interpolating multivariate functions. I'm not set on using Chebyshev polynomials, I have just had some exposure to them and know they tend to be efficient (in terms of # of necessary coefficients and interpolation error).
I was wondering if anyone could give me (an engineer) any pointers for how to go about interpolating a multi-variate function? Simple examples or sample code would be awesome, but I'll take any attempts to explain how interpolation would work in higher dimensions, including (readable) references.