Proceedings Article10.1109/PDCAT.2008.21
A Parallel Algorithm for Block Tridiagonal Systems
Heng Zhang,Wu Zhang,Xian-He Sun +2 more
- 01 Dec 2008
- pp 62-65
3
TL;DR: A parallel algorithm, namely parallel block diagonal dominant (PBDD) algorithm, is proposed to solve block tridiagonal linear systems on multi-computers based on divided-and-conquer idea of the PDD method.
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Abstract: A parallel algorithm, namely parallel block diagonal dominant (PBDD) algorithm, is proposed to solve block tridiagonal linear systems on multi-computers. This algorithm is based on divided-and-conquer idea of the PDD method. When the systems is strictly block diagonal dominant, the PBDD is highly parallel and provides approximate solutions that equals to the exact solutions within machine accuracy. The PBDD method has been implemented on a 64-node multi-computer. The analytic results match closely with the results measured from the numerical experiments.
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Citations
Research note: Revisiting parallel cyclic reduction and parallel prefix-based algorithms for block tridiagonal systems of equations
TL;DR: A critical block size that separates these two regions is shown to emerge and its dependence both on problem dependent parameters and on machine-specific constants is established.
20
A Parallel Multi-layer Hybrid Algorithm for solving block-tridiagonal systemes
Heng Zhang,Zhang Wu +1 more
- 01 Dec 2011
TL;DR: Theoretical analyses and numerical experiments indicate that PMHB is an efficient and arbitrarily extensible method with multi-layer hybrid cycle reduction calculation, and parallel efficiency over 90 % is reached.
2
The Parallel Block Odd-Even Reduction Algorithm for Block Tridiagonal Systems
Heng Zhang,Wu Zhang +1 more
- 28 Dec 2009
TL;DR: The PBOER algorithm is the combination of PDD and OER method, and is thus highly accurate and scalable, and provides approximate solutions that equals to the exact solutions within machine accuracy.
1
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TL;DR: The PDD algorithm is highly parallel and provides an approximate solution which equals the exact solution within machine accuracy, which closely match the results measured from the nCUBE-1 machine.