Function for Smoothing spline approximation

Hello, I have a 3-dimensional function f(x1,x2,x3)=x1^2+x2^2+x3^2. (x1,x2,x3) is a vector with components x1, x2 and x3. Therefore my input is a matrix including these vectors. I need to approximate this function and search for a matlab-function like smoothingspline=smoothingFunction(matrx with input values,function f,smoothingparam_lambda) ; As output of this function I expect set of values from the approximated function for each input vector. Does something like this exist in matlab?

Maybe the info that such kind of function already exists in R and is called tps() does help.

I would be very happy if you can help me to find this smoothing function in Matlab. Thank you in advance Kind Regards

Answer 1

[Mark Stone]

This was originally a comment, but no one has answered, so here is a partial answer.

It would seem your challenge is the need for trivariate smoothing spline. The Curve Fitting toolbox has functions for bivariate smoothing splines, but not as far as I can tell for trivariate or general multivariate smoothing spline. Trivariate (and higher) tensor product splines can be accommodated however, at least for data on a rectangular grid (as opposed to irregularly spaced data). You'll need to determine whether that meets your needs.

[Mark Stone]

I presume that the function f(x1,x2,x3)=x1^2+x2^2+x3^2 is just for illustrative purposes, and that your actual data will not be the result of evaluation from such a simple, and smoooooth function, otherwise what's the point of developing a (smoothing) spline approximation, unless it is just for the heck of it or an assignment.