Computation of Uniform Recurrence Equations over Finite Domains (1993)
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BibTeX
@TECHREPORT{Aldrich93computationof,
author = {William J. Aldrich and P. R. Kumar},
title = {Computation of Uniform Recurrence Equations over Finite Domains},
institution = {},
year = {1993}
}
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Abstract
Uniform recurrence equations arise frequently in scientific problems. We examine the problem of evaluating a given set of recurrence functions on an arbitrary finite set of index points. We provide a necessary and sufficient condition to determine when the equations can be grouped by index points into batch sets, for all finite domains, such that the batch sets can be sequentially evaluated. We show how the batch sets can be ordered using the hyperplane method. Next we provide a necessary and sufficient condition to determine when one can "index shift" a set of recurrence equations so that it is batch computable for all finite domains. Finally, we provide an algorithm for performing an index shifting that enables all of the computations within a batch to be performed in parallel. Index terms: Finite Domains, Hyperplane Method, Parallel Computation, Scientific Computation, Uniform Recurrence Equations The research reported here has been supported in part by the U.S. Army Research Of...
