An out-of-core sparse Cholesky solver
An out-of-core sparse Cholesky solver
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DOI：
10.1145/1499096.1499098
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发表时间：
2009-03
期刊：
影响因子：
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通讯作者：
J. Reid;J. Scott
中科院分区：
文献类型：
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作者：
J. Reid;J. Scott
求解大型稀疏线性方程式系统的直接方法由于其通用性和鲁棒性而流行。他们的主要弱点是，他们需要的记忆通常会随着问题大小而迅速增加。我们讨论了新的对称直接求解器的首次版本的设计和开发，该求解器旨在通过允许系统矩阵，中间数据和矩阵因子在外部存储来规避此限制。该代码用Fortran编写并称为HSL_MA77，实现了多额定算法。第一个版本是针对正定系统的，并执行潮汐分解。特别注意使用有效的密集线性代数内核代码，该代数处理正面矩阵上的全矩阵操作以及输入/输出操作。输入/输出操作是使用提供虚拟内存系统的单独软件包执行的，并允许数据分布在许多文件上；对于非常大的问题，这些可能会在多个设备上保存。给出了30个大型现实世界问题的收集数值结果，所有这些问题均已成功解决。
Direct methods for solving large sparse linear systems of equations are popular because of their generality and robustness. Their main weakness is that the memory they require usually increases rapidly with problem size. We discuss the design and development of the first release of a new symmetric direct solver that aims to circumvent this limitation by allowing the system matrix, intermediate data, and the matrix factors to be stored externally. The code, which is written in Fortran and called HSL_MA77, implements a multifrontal algorithm. The first release is for positive-definite systems and performs a Cholesky factorization. Special attention is paid to the use of efficient dense linear algebra kernel codes that handle the full-matrix operations on the frontal matrix and to the input/output operations. The input/output operations are performed using a separate package that provides a virtual-memory system and allows the data to be spread over many files; for very large problems these may be held on more than one device. Numerical results are presented for a collection of 30 large real-world problems, all of which were solved successfully.