I was looking for approaches on how to adequately interpolate the values for a continuous 3D function for which I have the exact values in a 3D grid of equidistant points. I found that linear interpolation in 3D works well but I lose some precision. So I found Gauss interpolation, mentioned here
http://mathworld.wolfram.com/GausssInterpolationFormula.html
my first question; for the coefficient expression, are the two terms multiplied or summed?
I was looking for an online reference with all the information but found anything. Lastly I wonder how could I use this idea for the 3D mesh of points mentioned before. I guess I would get first the individual values in one dimension for the function, and then get the 3D value directly from them.
Last, I wonder which similar and accurate methods could you recommend me. I heard about Chebyshev method and some other, but I am not sure abut their accuracy.