Parallel sparse matrix vector multiply software for matrices with data locality

Tuminaro, Raymond S.; Shadid, John N.; Hutchinson, S.A.

doi:10.1002/(sici)1096-9128(199803)10:3<229::aid-cpe296>3.0.co;2-i

Cited by 24 publications

(12 citation statements)

References 15 publications

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“…Operating on such dense blocks considerably reduces the amount of indirect addressing required for MVP. This improves the performance dramatically on vector machines [7] and also remarkably on superscalar architectures [8]. The block based algorithm for MVP is listed in Fig.…”

Section: Operating On Dense Blocksmentioning

confidence: 92%

Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Tiyyagura

Küster

Borowski³

2006

Computational Science – ICCS 2006

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Abstract. Many applications based on finite element and finite difference methods include the solution of large sparse linear systems using preconditioned iterative methods. Matrix vector multiplication is one of the key operations that has a significant impact on the performance of any iterative solver. In this paper, recent developments in sparse storage formats on vector machines are reviewed. Then, several improvements to memory access in the sparse matrix vector product are suggested. Particularly, algorithms based on dense blocks are discussed and reasons for their superior performance are explained. Finally, the performance gain by the presented modifications is demonstrated.

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Section: Operating On Dense Blocksmentioning

confidence: 92%

Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Tiyyagura

Küster

Borowski³

2006

Computational Science – ICCS 2006

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“…In this setting, the common algorithm [13,33,34] executes the following steps at each processor P k :…”

Section: Ax B By Settingmentioning

confidence: 99%

Parallel image restoration using surrogate constraint methods

Uçar

Aykanat

Pınar

et al. 2007

Journal of Parallel and Distributed Computing

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When formulated as a system of linear inequalities, the image restoration problem yields huge, unstructured, sparse matrices even for images of small size. To solve the image restoration problem, we use the surrogate constraint methods that can work efficiently for large problems. Among variants of the surrogate constraint method, we consider a basic method performing a single block projection in each step and a coarse-grain parallel version making simultaneous block projections. Using several state-of-the-art partitioning strategies and adopting different communication models, we develop competing parallel implementations of the two methods. The implementations are evaluated based on the per iteration performance and on the overall performance. The experimental results on a PC cluster reveal that the proposed parallelization schemes are quite beneficial.

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“…Operating on such dense blocks considerably reduces the amount of indirect addressing required for sparse MVP [6]. This improves the performance of the kernel dramatically on vector machines [9] and also remarkably on superscalar architectures [10,11]. BLIS uses this approach primarily to reduce the penalty incurred due to indirect memory access.…”

Section: Block-based Linear Iterative Solver (Blis)mentioning

confidence: 99%

Block-Based Approach to Solving Linear Systems

Tiyyagura

Küster

2007

Computational Science – ICCS 2007

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Abstract. This paper addresses the efficiency issues in solving large sparse linear systems parallely on scalar and vector architectures. Linear systems arise in numerous applications that need to solve PDEs on complex domains. The major time consuming part of large scale implicit Finite Element (FE) or Finite Volume (FV) simulation is solving the assembled global system of equations. First, the performance of widely used public domain solvers which target performance on scalar machines is analyzed on a typical vector machine. Then, a newly developed parallel sparse iterative solver (Block-based Linear Iterative Solver -BLIS) targeting performance on both scalar and vector systems is introduced and the time needed for solving linear systems is compared on different architectures. Finally, the reasons behind the scaling behaviour of parallel iterative solvers is analysed.

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Parallel sparse matrix vector multiply software for matrices with data locality

Cited by 24 publications

References 15 publications

Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Parallel image restoration using surrogate constraint methods

Block-Based Approach to Solving Linear Systems

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