Parallel Sparse Matrix Computations

并行稀疏矩阵计算

• 批准号: 9412698
• 负责人: Alex Pothen
• 金额: $ 15.25万
• 依托单位: Old Dominion University Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9412698&HistoricalAwards=false
• 关键词: Parallel; Sparse; Matrix; Computations

This project investigates the design, implementation, analysis of algorithms for several problems that arise in the solution of large, sparse systems of equations and least squares problems on high-performance parallel computers. The irregular nature of the memory access required by sparse matrix algorithms makes good performance difficult to achieve. Innovative algorithmic approaches capable of better concurrency than the traditional sequential approaches, and implementations that exploit the memory hierarchy are essential to obtain good performance. The following problems are being investigated: (1) An algebraic approach to the partitioning problem that arises in partitioning data and computation on parallel computers, and in computing nested dissection orderings, (2) The problem of reordering sparse matrices to minimize with applications to computing incomplete factorization (3) The product-form-inverse approach to the solution of sparse triangular systems on parallel computers, (4) The solution of rank-deficient least-squares problems on sequential and parallel computers.

本项目研究了设计，实施， 分析算法中出现的几个问题， 大型稀疏方程组和最小二乘法的解 高性能并行计算机上的问题。 的不规则性 稀疏矩阵算法所需的存储器访问使得性能良好 很难实现。 创新的算法方法能够更好地 与传统的顺序方法相比， 利用存储器层次结构的实现是 对于获得良好的性能至关重要。 以下问题正在 研究：（1）一个代数方法的分区问题， 在并行计算机上划分数据和计算时出现， （2）稀疏矩阵的重排序问题， 应用于计算不完全因式分解 (3)乘积形式逆法求解 稀疏三角形方程组的秩亏最小二乘问题的求解 串行和并行计算机。