A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
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DOI：
10.1137/s1064827595294691
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发表时间：
1998-05
期刊：
影响因子：
--
通讯作者：
M. Benzi;M. Tuma
中科院分区：
文献类型：
--
作者：
M. Benzi;M. Tuma
本文关注一种针对大型稀疏线性系统预处理的新方法。开发了一种计算非对称矩阵逆的不完全分解的过程，并且将得到的分解后的稀疏近似逆用作共轭梯度型方法的显式预处理器。讨论了预处理器的一些理论性质，并给出了对来自哈威尔 - 波音集合以及蒂姆·戴维斯集合的测试矩阵进行的数值实验。我们的结果表明，新的预处理器比其他近似逆预处理器构建成本更低。此外，新技术确保了预处理迭代的收敛速度与使用标准隐式预处理器所获得的收敛速度相当。
This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient--type methods. Some theoretical properties of the preconditioner are discussed, and numerical experiments on test matrices from the Harwell--Boeing collection and from Tim Davis's collection are presented. Our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners. Furthermore, the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners.