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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:

  1. Can you please let me any good reference for the approximation of multivariate functions?
  2. How can I use Chebychev polynomials for the multivariate function?

Regards, Reza

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    $\begingroup$ Does your model have a functional representation? Or, can it at least be evaluated on a regular grid? If so, then use tensor-product splines to interpolate. For scattered data use radial basis functions. $\endgroup$ – rych Sep 29 '14 at 4:30

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