Optimized interpolation method with fixed-location sample data points?

Question

I'm trying to find an optimized spatial interpolation method that deals with fixed-location sample data points. Say if I have fixed-location sampling sites and collect data daily, and then use these data to create interpolation surfaces.

Is there a method that pre-process the spatial relationships among those sampling sites and then integrate this spatial relationship into the interpolation method to speed up the whole interpolation process?

I searched some information but couldn't find what I want. Can anyone put me on the right direction?

Answer 1

I guess that you need to speed up the whole interpolation process for adding next day measurements. Hopefully enough optimization (pre-computing and updating) could be possible when you write down a suitable tensor-product spline interpolation problem over a regular 2d grid. Alternatively, you could see this as a 1d interpolation along time axis of a vector-valued function sampled daily with each sample consisting of an array of values at spatial sites.