This article is cited in 2 papers

Parametrized tiling: Accurate approximations and analysis of global dependences

S. V. Bakhanovich, P. I. Sobolevskii

Institute of Mathematics, National Academy of Sciences, ul. Surganova 11, Minsk, 220072, Belarus

Abstract: Aspects of parametrized tiling as applied to algorithms whose computational domain can be represented as a convex polyhedron are studied. A method for constructing approximations to a set of tiles is developed, and necessary and sufficient conditions for their accuracy are stated. Formulas for determining intertile vectors are derived. A formal representation of iteration sets generating such vectors is obtained in the form of polyhedra with explicitly expressed boundaries.

Key words: tiling, tile, distributed memory computer system, optimization, convex polyhedron.

UDC: 519.671

Received: 24.12.2013
Revised: 03.03.2014

DOI: 10.7868/S0044466914110039

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:11, 1748–1758

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