Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Parallel programming with MPI
Parallel algorithms for regular architectures: meshes and pyramids
Parallel algorithms for regular architectures: meshes and pyramids
CABAL: polynomial and power series algebra on a parallel computer
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Experience with FORMAC algorithm design
Communications of the ACM
MPI: The Complete Reference
New recursive minor expansion algorithms
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Arithmetic complexity of unordered sparse polynomials
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Parallelism in algebraic computation and parallel algorithms for symbolic linear systems
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
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We describe a set of representations for polynomials and sparse matrices suited for use with fine-grain parallelism on a distributed memory multiprocessor system. Our aim is to support use of supercomputers with this style of architecture to perform computations that would exceed the main memory capacity of more traditional computers: although such systems have very high performance communication networks it is still essential to avoid letting any one part of the network become a bottleneck. We use randomised data placement both to avoid hot-spots in the communication patterns and to balance (in a probabilistic sense) the memory load placed upon each processing element. The expected application areas for such a system will be those where intermediate expression swell means that the huge primary memory available on MPP systems will be needed if the smaller final result is to be successfully computed.