Process scheduling in DSC and the large sparse linear systems challenge

Díaz, A.; Hitz, Markus A.; Kaltofen, Erich; Lobo, Austin; Valente, Thomas W.

doi:10.1007/bfb0013169

Cited by 7 publications

(4 citation statements)

References 12 publications

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“…In that situation, Proposition 3 could be relaxed. If the rank of (4) were one or two less than the rank of (7), with probability 1/2 or 1/4 we still would find a solution to (7). For very large finite fields such a rank deficiency would make the problem quite infeasible.…”

Section: Resultsmentioning

confidence: 99%

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Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems

Kaltofen¹

1995

Math. Comp.

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By using projections by a block of vectors in place of a single vector it is possible to parallelize the outer loop of iterative methods for solving sparse linear systems. We analyze such a scheme proposed by Coppersmith for Wiedemann's coordinate recurrence algorithm, which is based in part on the Krylov subspace approach. We prove that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors. Our analysis is valid for fields of entries that have sufficiently large cardinality. Our analysis also deals with an arising subproblem of solving a singular block Toeplitz system by use of the theory of Toeplitz-like matrices.

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Section: Resultsmentioning

confidence: 99%

“…In that case we use "double blocking," where each of the computers processes blocks of 32 vectors by 32 bit logic. The details of this experiment are published in [7]. We have also applied the method to the problem of factoring polynomials of degree 10,000 and more over finite fields [11].…”

Section: Resultsmentioning

confidence: 99%

Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems

Kaltofen¹

1995

Math. Comp.

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“…The black box model for polynomials [40] and the parallel reconstruction algorithm via sparse interpolation seemed much more practicable-embarrassingly parallel. Thus in 1990 we began developing a run-time support tool, DSC (Distributed Symbolic Computation) [10,8]. Several features in DSC seem unsupported in commonly used distributed run-time support tools, such as MPI/PVM.…”

Section: A Brief History Of My Research In Parallel Symbolic Computationmentioning

confidence: 99%

Fifteen years after DSC and WLSS2 what parallel computations I do today

Kaltofen

2010

Proceedings of the 4th International Workshop on Parallel and Symbolic Computation

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A second wave of parallel and distributed computing research is rolling in. Today's multicore/multiprocessor computers facilitate everyone's parallel execution. In the mid 1990s, manufactures of expensive main-frame parallel computers faltered and computer science focused on the Internet and the computing grid. After a ten year hiatus, the Parallel Symbolic Computation Conference (PASCO) is awakening with new vigor.I shall look back on the highlights of my own research on theoretical and practical aspects of parallel and distributed symbolic computation, and forward to what is to come by example of several current projects. An important technique in symbolic computation is the evaluation/interpolation paradigm, and multivariate sparse polynomial parallel interpolation constitutes a keystone operation, for which we present a new algorithm. Several embarrassingly parallel searches for special polynomials and exact sum-of-squares certificates have exposed issues in even today's multiprocessor architectures. Solutions are in both software and hardware. Finally, we propose the paradigm of interactive symbolic supercomputing, a symbolic computation environment analog of the STAR-P Matlab platform.

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“…It is a crossplatform language so that the applications can be run in any platform or any operating system. Symbolic computation [2,3] is a Computer Algebra System which takes the mathematical expression using alphabets, numeric characters and symbolic notations and parses the expression using a recursive parser and finally gives the output. A Mathematical Pseudo Language [4] is used to interpret the symbolic expressions and convert it into a string which is actually given to the parser.…”

Section: Introductionmentioning

confidence: 99%

Implementation of Recursive Structural Parser for Symbolic Computation using Mathematical Pseudo Language and Features of Java

SudiptaAchary¹,

Reza²

2012

IJCA

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Symbolic Computation is a Computer Algebra System (CAS) which is developed to compute the symbolic mathematical expressions consisting simple or complex calculations. Symbolic Computation provides the interface to provide input expression in a typical mathematical format. Mathematical problems related to algebra, logarithm, roots, sum & product of series etc can be solved using this package.Use of Object Oriented programming on JAVA platform provides an efficient method to such calculations. GUI components like Panels, Applets, Menus, and Buttons from AWT package are used to make the GUI simple and user friendly. The GUI is made in such a way that it takes input in a typical mathematical format which is helpful for anyone to compute expressions without using complex instructions or commands. This paper represents a strong yet simple way to solve mathematical problems by representing expressions using Symbols and characters with the concept of pseudo language.

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Process scheduling in DSC and the large sparse linear systems challenge

Cited by 7 publications

References 12 publications

Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems

Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems

Fifteen years after DSC and WLSS2 what parallel computations I do today

Implementation of Recursive Structural Parser for Symbolic Computation using Mathematical Pseudo Language and Features of Java

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