Open AccessJournal Article
Solving linear systems with vectorized WZ factorization.
TL;DR: The results of numerical experiments which show that vectorization accelerates the sequential WZ factorization of a matrix which was implemented with the BLAS1 library.
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Abstract: In the paper we present a vectorized algorithm for WZ factorization of a matrix which was implemented with the BLAS1 library. We present the results of numerical experiments which show that vectorization accelerates the sequential WZ factorization. Next, we parallelized both algorithms for a two-processor shared memory machine using the OpenMP standard. We present performances of these four algorithms on a two-Pentium III machine with a Linux system (the parallelized sequential algorithm is better than the normal sequential one, but the parallelized vectorized algorithm is very similar in its performance to the non-parallelized vectorized one).
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Citations
The Vectorized and Parallelized Solving of Markovian Models for Optical Networks
Beata Bylina,Jarosław Bylina +1 more
- 06 Jun 2004
TL;DR: The article presents two approaches to the WZ factorization – specific ones for solving Markov chains – and the results of their vectorization and parallelization.
The inverse iteration with the WZ factorization used to the Markovian models
TL;DR: The paper contains the theoretical base of the method, numerical experiment results where the accuracy and the performance time were investigated, and a modified (with the use of the SBLAS library and the Harwell-Boeing sparse matrix storage scheme) method.
Double power method iteration for parallel eigenvalue problem
K. Rhofir,M. Ameur,A. Radid +2 more
TL;DR: In this article, the double power iteration method was introduced, which can be seen as an extension of the classical power iteration in the sense that they calculate the two dominants eigenvalues at each stage.
Empirical Performance Evaluation of Gaussian Elimination and Parallel Implicit Elimination with Parallel Computing Technologies
Bilal A. Tuama
- 01 Nov 2018
TL;DR: The speedup of PIE method is better than GE method by increasing number of processors but the efficiency will be decrease gradually because the complexity at each node.
2
A parallel algorithm to solve symmetric tridiagonal linear systems
Yan Zhong,Zhi-Gang Luo,Feng Wu +2 more
- 21 May 2010
TL;DR: A parallel algorithm is provided for symmetric tridiagonal linear systems with coefficient matrices of classical structure based on WZ factorization and it can be concluded that the method is effective in load balance and efficiency.
1
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TL;DR: The main objective of this paper is to present a characterization for the existence of the WZ factorization and prove uniqueness of the factorization.
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TL;DR: The parallel WZ matrix factorisation is presented, and numerical results to confirm the superiority of WZ over the LV method are presented.
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David J. Evans,M. Barulli +1 more
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