A cancellation free algorithm, with factoring capabilities, for the efficient solution of large sparse sets of equations

Smit, Jaap

doi:10.1145/800206.806386

Cited by 17 publications

(5 citation statements)

References 18 publications

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“…The identities given Such considerations are indeed artificial, only being attempts to retrieve the original structure of the problem. Our experience with NETFORM stipulates that this kind of problems requires structure preserving techniques [13,14]. Figure 2 also illustrates that (forthcoming) improvements of our code optimization facilities.…”

Section: Error Messages and Warningsmentioning

confidence: 93%

An expression analysis package for REDUCE

Hulzen

Hulshof

1982

SIGSAM Bull.

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Section: Error Messages and Warningsmentioning

confidence: 93%

An expression analysis package for REDUCE

Hulzen

Hulshof

1982

SIGSAM Bull.

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“…Our application area is symbolic linear algebra, and specifically the calculation of determinants of sparse symbolic matrices [11,10]. Because the structures needed to represent the sparse matrices are fairly compact we keep a copy of them in each PE so that this information at least does not need repeated broadcast.…”

Section: Polynomial and Matrix Representationsmentioning

confidence: 99%

A Parallel Symbolic Computation Environment: Structures and Mechanics

Matooane

Norman

1999

Euro-Par’99 Parallel Processing

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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.

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“…[21], and Wang [23]. It must be observed that although sparse systems have sparse rational solutions, the power series solutions need not be sparse (e.g., l/( 1 -z + z*') has a dense power series representation).…”

Section: 2)mentioning

confidence: 99%

Systems of linear equations with dense univariate polynomial coefficients

Cabay

1987

J. ACM

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An algorithm for computing the power series solution of a system of linear equations with components that are dense univariate polynomials over a field is described and analyzed. A method for converting the power series solution to rational form is derived. Theoretical and experimental cost estimates are obtained and used to identify classes of problems for which the power series method outperforms modular methods. Finally, it is shown that the power series method also provides an effective mechanism for solving the problem in which the coefficients of the polynomials are from the ring of integers.

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A cancellation free algorithm, with factoring capabilities, for the efficient solution of large sparse sets of equations

Cited by 17 publications

References 18 publications

An expression analysis package for REDUCE

An expression analysis package for REDUCE

A Parallel Symbolic Computation Environment: Structures and Mechanics

Systems of linear equations with dense univariate polynomial coefficients

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