On using Radial Basis Functions to approximate nonlinear data set

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I have a two dimensional function represented by 3 data set

$f_i(\omega_i,\beta_i)=\psi_i$ such that $i \in [1,N]$

How can I do the following:

  • First interpolate to larger data points using Radial Basis Function but want to increase the interpolating points such $ g_k \equiv f_i $ with $ k \in [1,M] ; M > N $
  • Approximate $g$ using Radial Basis Functions or Similar algorithm for reconstructing the function.