Solving large dense systems of linear equations on systems with virtual memory and with cache

Lioen, W.M.; Winter, D.T.

doi:10.1016/0168-9274(92)90056-j

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…In order to compare different algorithms to solve a system of equations Ax=b with A ∈ ℝ n×n and B ∈ ℝ n , the O(n p ) of them are noted in table 3 [15]. In detail, the computational work involved in an QR Factorization is of order 2n 3 + O(n 2 ).…”

Section: Figure 2: S Olution Of System Of Linear Equations With Paralmentioning

confidence: 99%

A Parallel implementation of Gram-Schmidt Algorithm for Dense Linear System of Equations

Ghodsi¹,

Mehri²,

Taeibi-Rahni³

2010

IJCA

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The linear system of equations with dense coefficient matrix is very common in science and engineering. In this paper, a parallel algorithm based on Gram-Schmidt QR factorization method for the exact solution of dense system of linear equations is presented. Although several parallel approaches have been proposed to solve the system of linear equations until now, the aim of this paper is to show the ability and limitation of this parallel algorithm in comparison with the sequential one. The suggested parallel algorithm is executed on M IM D architecture and distributed memory. In order to specify the efficiency of this algorithm, the amounts of speedup and FLOPs in executions with different size of matrix (from 2000 to 12000 equations) on up to 5 processors are compared together. The results show that the achieved speedup is significant, and also the performance of this practical parallel algorithm increases as the number of equations grows.

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Section: Figure 2: S Olution Of System Of Linear Equations With Paralmentioning

confidence: 99%

A Parallel implementation of Gram-Schmidt Algorithm for Dense Linear System of Equations

Ghodsi¹,

Mehri²,

Taeibi-Rahni³

2010

IJCA

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A Novel Parallel Algorithm Based on the Gram‐Schmidt Method for Tridiagonal Linear Systems of Equations

Ghodsi

Taeibi-Rahni

2010

Mathematical Problems in Engineering

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This paper introduces a new parallel algorithm based on the Gram-Schmidt orthogonalization method. This parallel algorithm can find almost exact solutions of tridiagonal linear systems of equations in an efficient way. The system of equations is partitioned proportional to number of processors, and each partition is solved by a processor with a minimum request from the other partitions' data. The considerable reduction in data communication between processors causes interesting speedup. The relationships between partitions approximately disappear if some columns are switched. Hence, the speed of computation increases, and the computational cost decreases. Consequently, obtained results show that the suggested algorithm is considerably scalable. In addition, this method of partitioning can significantly decrease the computational cost on a single processor and make it possible to solve greater systems of equations. To evaluate the performance of the parallel algorithm, speedup and efficiency are presented. The results reveal that the proposed algorithm is practical and efficient.

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Solving large dense systems of linear equations on systems with virtual memory and with cache

Cited by 2 publications

References 12 publications

A Parallel implementation of Gram-Schmidt Algorithm for Dense Linear System of Equations

A Parallel implementation of Gram-Schmidt Algorithm for Dense Linear System of Equations

A Novel Parallel Algorithm Based on the Gram‐Schmidt Method for Tridiagonal Linear Systems of Equations

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