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\[
  f(x,y) = \sum_{j=0}^{M-1} f_j \phi_j(x, y) 
\]


\[
  \min_f \sum_{i=0}^{N-1} (f(x_i, y_i) - z_i)^2 \ + \ \alpha \int_\Omega (\nabla f)^2 \, dx dy
\]



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