I have a mathematical model for a complex system which I would like to approximate it. My idea is to run this complex model once and produce some outputs, and then fit a polynomial for these outputs. However, my model has several inputs and I can not use known smooth polynomials, e.g. Chebyshev, easily. On the other hand I also want to avoid solving an optimization problem to fit a polynomial to the outputs.
I have two questions:
- Can you please let me any good reference for the approximation of multivariate functions?
- How can I use Chebychev polynomials for the multivariate function?