Reducing Interpolation on Multi-Grid to Quantizing Grid's Data-Base as a Recursion

In his article “Powerlist: A Structure for Parallel Recursion” Jayadev Misra wrote: “Many data parallel algorithms – Fast Fourier Transform, Batcher’s sorting schemes and prefix sum – exhibit recursive structure. We propose a data structure, powerlist, that permits succinct descriptions of such algorithms, highlighting the roles of both parallelism and recursion. Simple algebraic properties of this data structure can be exploited to derive properties of these algorithms and establish equivalence of different algorithms that solve the same problem.” The quote above illustrates a commonly shared assumption regarding recursion implementatations: either they are done in purely structural terms or they cannot be done at all. Multi-dimensional interpolation on a grid is one of hosts of semi-recursive schemes that, while routinely referred to as recursive and often described in semi-recursive terms, cannot be implemented as a recursion in their structural entirety. This article describes structural framework for and a computer implementation of a computer implemented scheme that isolates the recursive core of interpolation on a multi-grid, an arrangement that breaks down into to a number of interpolation optimization techniques which, once implemented, provide gains in multi-interpolation speed that, compared to some known benchmarks, measure in multiple orders of magnitude.