Proceedings Article10.1109/ICFCC.2010.5497408
A parallel algorithm to solve symmetric tridiagonal linear systems
Yan Zhong,Zhi-Gang Luo,Feng Wu +2 more
- 21 May 2010
- Vol. 2
1
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.
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Abstract: For linear systems with coefficient matrices of classical structure, WZ factorizations for matrices are basic mathematical theories to design a class of parallel algorithms. Based on WZ factorization, a parallel algorithm is provided for symmetric tridiagonal linear systems. The method estimates the computation task carefully so that it assigns the system skillfully to get even load balance. In addition, the algorithm makes full use of the overlap between computation and communication to reduce waiting time in each processor. Both the subsystem assigned in each processor and the reduced subsystem have the same computing logic, as a result, a two-level method forms. By theory analysis and experiment results, it can be concluded that our method is effective in load balance and efficiency.
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Citations
On parallelizing analysis of power systems in cloud environment
Wanxing Sheng,Keyan Liu,Song Jin,Weiyue Zhao,Wei Tang +4 more
- 01 Oct 2016
TL;DR: This paper parallelize power flow calculation based on Map-Reduce programming framework and evaluates the efficiency, finding that the effectiveness of the proposed scheme is demonstrated.
2
References
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S. Chandra Sekhara Rao
- 01 Aug 1997
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.
40
Implicit matrix elimination (IME) schemes
TL;DR: New implicit (2 × 2) matrix elimination schemes are introduced and their relationship to the well known LU and parallel WZ factorisation schemes demonstrated.
19
The Choleski Q.I.F. algorithm for solving symmetric linear systems
TL;DR: A matrix factorisation method based on the product of quadrant interlocking factors (Q.I.F.) which can be denoted mnemonically as W and Z and are of ‘butterfly’ or bow-tie form when the given matrix is symmetric then the factorisation resolves into a more simpler form i.e., A = WW T.
14
Parallel solution of large symmetric tridiagonal linear systems
S. Chandra Sekhara Rao,Sarita +1 more
- 01 Mar 2008
TL;DR: A matrix factorization called WZ factorization for the solution of symmetric tridiagonal linear systems is presented and when combined with partitioning scheme, it renders a divide and conquer algorithm.
13
•Journal 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.