Parallel algorithms for sparse triangular system solution

Kumar, P. Sreenivasa; Kumar, M. Kishore; Basu, Anupam

doi:10.1016/0167-8191(93)90048-p

Cited by 7 publications

(5 citation statements)

References 10 publications

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“…Apart from matrix transpose, permutation communication patterns also arise frequently in other HPC applications such as binary-exchange based fast-fourier transforms [6] and recursive doubling for MPI collectives in MPICH [11]. Our techniques are also useful in other applications that involve permutation communication.…”

Section: Fig 1 Illustration Of Sdr Technique and Routing Algorithmsmentioning

confidence: 95%

Optimizing Matrix Transpose on Torus Interconnects

Chakaravarthy

Jain

Sabharwal

2010

Euro-Par 2010 - Parallel Processing

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Abstract. Matrix transpose is a fundamental matrix operation that arises in many scientific and engineering applications. Communication is the main bottleneck in performing matrix transpose on most multiprocessor systems. In this paper, we focus on torus interconnection networks and propose application-level routing techniques that improve load balancing, resulting in better performance. Our basic idea is to route the data via carefully selected intermediate nodes. However, directly employing this technique may lead to worsening of the congestion. We overcome this issue by employing the routing only for selected set of communicating pairs. We implement our optimizations on the Blue Gene/P supercomputer and demonstrate up to 35% improvement in performance.

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Section: Fig 1 Illustration Of Sdr Technique and Routing Algorithmsmentioning

confidence: 95%

Optimizing Matrix Transpose on Torus Interconnects

Chakaravarthy

Jain

Sabharwal

2010

Euro-Par 2010 - Parallel Processing

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“…They extend their method to a distributed-memory computer where the columns of L are distributed across the processors (George et al 1989a). Kumar, Kumar and Basu (1993) extend this method by exploiting the dependency structure with the elimination tree, rather than using the larger structure of the graph of L.…”

Section: Parallel Triangular Solvementioning

confidence: 99%

“…1989 a ). Kumar, Kumar and Basu (1993) extend this method by exploiting the dependency structure with the elimination tree, rather than using the larger structure of the graph of .…”

Section: Other Topicsmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

171

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Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1 This informal yet practical definition captures the essence of the goal of direct methods for solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.

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“…More Gcently, attempts to exploit parallelism in triangular systems related to sparse matrices have been made in [6,7]. In both cases, the basic approach is to parallelize the forward (or backward) substitution process using the adjacency graph of L. Results presented in 161 compare the heights of the elimination tree, using MDO and the proposed partitioning algorithm.…”

Section: Introductionmentioning

confidence: 98%

“…In [7], parallel triangular system solvers are proposed which use the elimination tree structure and combined with the idea presented in [8] for dense matrices. Corresponding results for the forward solver shows a speed-up of 3.39, 5.46 and 5.32 on 4-, 8-and 16-processors for a grid of size 65, while for the backward solver, a speed-up of 3.37, 4.35 and 4.65 is exhibited for 4-, 8-and 16-processors for a 65 x 65 grid.…”

Section: Introductionmentioning

confidence: 99%