@DavidB

So, in a nutshell, this algorithm is for cubic interpolation in multiple dimensions?

Not quite (but maybe close enough): it is a weighted sum of interpolants where the weights are w.r.t. distance from interpolation point(IP)

and are zero outside a given radius from the IP. The interpolants can take several forms: linear, quadratic, cubic.

Now that I have some context for this routine, I can better research it.

If you have access to the ACM Digital Library you can download the source material (SHEPPACK) and try it out.

(Don't want to be salesy on this forum, but you could ask NAG Support for a trial licence of NAG Fortran, C or

MATLAB Library and start with the example programs for the e01{s,t,z}* routines there)

A related question: does this routine get much use?

Or are its applications highly specialized and, therefore, rarely used?

I can tell you that NAG added routines for 4, 5 and >5 dimensions in recent Marks of its libraries because of

special requests for these. So yes they are currently being used.

@CyLith

Just for my own edification, why use radial basis function instead of, say, computing a Delaunay triangulation on the points and using spline interpolation (linear or higher order)? I'm genuinely curious about the applications of something like toms790.

Yes, triangulation and interpolation within a containing triangle is a popular option we have found.

The appropriate choice is dependent on the nature of the data being interpolated. Shepard algorithms

are generally robust; the smoothing over interpolants means that non-smooth noisy data can still

produce a reasonable global approximating function.