Towards Stable Mixed Pivoting Strategies for the Sequential and Parallel Solution of Sparse Symmetric Indefinite Systems
Towards Stable Mixed Pivoting Strategies for the Sequential and Parallel Solution of Sparse Symmetric Indefinite Systems
复制标题
稀疏对称不定系统顺序并行解的稳定混合枢轴策略
DOI：
10.1137/050629598
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Pralet
中科院分区：
文献类型：
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作者：
I. Duff;S. Pralet
我们考虑稀疏对称不确定矩阵的直接解。我们开发了新的枢纽策略，这些策略结合了数值枢纽和扰动技术。然后，迭代精炼过程使用我们的近似分解来计算解决方案。我们表明，我们的枢纽策略在数值上是鲁棒的，需要迭代精致的几个步骤，并且分解比以前的方法要快得多。此外，我们提出了专为平行分布分解而设计的原始方法。我们并行实施的关键点是对生长因子的廉价估计。该估计基于非对角线条目的近似值，不需要任何补充消息。
We consider the direct solution of sparse symmetric indefinite matrices. We develop new pivoting strategies that combine numerical pivoting and perturbation techniques. Then an iterative refinement process uses our approximate factorization to compute a solution. We show that our pivoting strategies are numerically robust, that few steps of iterative refinement are required, and that the factorization is significantly faster than with previous methods. Furthermore, we propose original approaches that are designed for parallel distributed factorization. A key point of our parallel implementation is the cheap and reliable estimation of the growth factor. This estimation is based on an approximation of the off-diagonal entries and does not require any supplementary messages.
影响因子：
2.1
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