## What mathematical methods work for interpolation 2d to 2d functions? [closed]

So we had a matrix like $$\matrix{12,32\cr24,12\cr..., ... \cr}$$ with length $N*2$ and another matrix $$\matrix{44,32\cr44,19\cr..., ... \cr}$$ with length $N*2$ and there is some function $f(x, y)$ that returns $z, t$. That 2 matrices that we were given represent known value pairs for $x,y$ and $z,t$ What are interpolation formulas that would help in such case?

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 Consider posting at math.stackexchange.com/questions?sort=newest but first, please read meta.mathoverflow.net/discussion/1125/… – Will Jagy Oct 16 2011 at 23:05 asked here math.stackexchange.com/questions/73173/… – Ole Jak Oct 17 2011 at 0:53