Fast 3D Block Parallelisation for the Matrix Multiplication Prefix Problem

K. Waldherr, T. Huckle (), T. Auckenthaler, U. Sander and T. Schulte-Herbrüggen ()
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K. Waldherr: TU Munich, Dept. of Computer Science
T. Huckle: TU Munich, Dept. of Computer Science
T. Auckenthaler: TU Munich, Dept. of Computer Science
U. Sander: TU Munich, Dept. of Chemistry
T. Schulte-Herbrüggen: TU Munich, Dept. of Chemistry

A chapter in High Performance Computing in Science and Engineering, Garching/Munich 2009, 2010, pp 39-50 from Springer

Abstract: Abstract For exploiting the power of supercomputers like the HLRB II cluster, developing parallel algorithms becomes increasingly important. The matrix prefix problem belongs to a class of issues lending themselves for parallelisation. We compare the tree-based parallel prefix scheme, which is adapted from a recursive approach, with a sequential multiplication scheme where only the individual matrix multiplications are parallelised. We show that this fine-grain approach outperforms the parallel prefix scheme by a factor of 2−3 and also leads to less memory requirements. Unlike the tree-based scheme, the fine-grain approach enables many options in the choice of the number of parallel processors and shows a better speedup performance when increasing the matrix sizes. The usage of the fine-grain approach in a quantum control algorithm instead of the coarse-grain approach allows us both to deal with systems of higher dimensions and to choose a finer discretisation.

Keywords: Matrix Multiplication; Quantum Control; Matrix Exponential; Block Operation; Fast Matrix Multiplication (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-13872-0_4

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DOI: 10.1007/978-3-642-13872-0_4

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