Which MATLAB toolbox should i use to aproximate the function of two variables?

I have:

x1=linspace(0,X,N); (i know X and N)

y1=linspace(0,Y,M); (i know Y and M, M is not equal to N)

I have matrix z with values z(x,y).I dont know z(x,y) explicitly. Dimension of that matrix is N x M.

x2=linspace(0,X,100*N);

y2=linspace(0,Y,100*M);

I want to evaluate matrix z2(x2,y2) (dimension 100*N x 100*M) that should represent the aproximation of function z.

I tried with the Curve Fitting app, but I did not succeed. The polynomial/lowess/interpolant fitting does not work well.

I cannot determine a model , so i cannot fit to one.

Is there any MATLAB toolbox that can help me with this (please provide help/example if there is)?

A link to file posted on file exchange solving this problem would be good as well.

Thanks, Petar

Answer 1

[Walter Roberson]

There are an infinite number of functions that fit any given finite list of points to within round off even supposing that the values have no noise. Because there are an infinite number, the probability that any given one is correct is 1/infinity which is 0.

Therefore what you ask cannot be done. Not unless you are willing to specify a finite list of forms of models to fit against.