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In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misrawrote:  "Many data parallel algorithms Fast Fourier Transform, Batcher's sortingschemes and prefix sum -exhibit recursive structure. We propose a datastructure, powerlist, that permits succinct descriptions of such algorithms,highlighting the roles of both parallelism and recursion. Simple algebraicproperties of this data structure can be exploited to derive properties ofthese algorithms and establish equivalence of different algorithms that solvethe same problem."  The quote above illustrates a widely shared assumption about recursionimplementations: either they are done in purely structural terms or they cannotbe done at all.  Multi-dimensional interpolation on a grid is one of hosts of semi-recursiveschemes that, while often referred to as recursive and routinely described invaguely recursive terms, cannot be implemented as a recursion in theirstructural entirety.  This article describes a computer-implemented scheme for isolating therecursive core of interpolation on a multi-grid, an arrangement that both stemsfrom and provides a structural framework to a number of multi-dimensionalinterpolation optimization techniques that, once implemented, provide gains inmulti-dimensional interpolation speed that, compared to some known benchmarks,measure in multiple orders of magnitude.  Categories and Subject Descriptors: Multi-dimensional Programming; ConcurrentProgramming; Recursion  General terms: Parallel Processing, Prioritized Processing, Interpolation,Recursion, Multi-Cube

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