I have already done linear interpolation in four variables and it works but the accuracy is not good, that's why I need to do non-linear interpolation for the same four variables.
Now, I have since learnt that one of the "easiest" ways to do it is by use of tensor product constructs.
Now, my question is, given, say, 4 univariate cubic polynomials (each of the 4 is interpolating its respective variable ), how does one multiply all four together ? (That is the definition of a tensor product construct in this context).
Thus, given the cubic polynomials,
var1 = aw^3 + bw^2 + bw + d
var2 = ex^3 + fx^2 + gx + h
var3 = iy^3 + jy^2 + ky + l
var4 = mz^3 + nz^2 + oz + p
F(w,x,y,z) = tensor product construct. How does one do that ?
Now please, no references to wikipedia articles -- or any other articles for that matter. I have read and re-read lots of articles online and at this point, they wont help --- what I need now is for someone who knows how to do a tensor product construct of the 4 univariate cases above to produce a multivariate case in 4 dimensions.