Foundations and Applications of Hierarchically stored Matrices

分层存储矩阵的基础和应用

• 批准号: 0702714
• 负责人: Robert van de Geijn
• 金额: --
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-15 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0702714&HistoricalAwards=false
• 关键词: Foundations; Applications; Hierarchically; stored; Matrices

With the advent of processors with multiple layers of cache and/or multiple processing cores it has become necessary to re-examine how matrices should be stored in memory. The investigators study how hierarchical data structures facilitate performance and reduce the programming effort when developing linear algebra libraries. Of particular interest is the impact on future multi-core processors, especially when the number of cores becomes large.The project pursues the theory and practice of algorithms for linear algebra operations, and their implementations, when the matrices and/or vectors are stored recursively by blocks (hierarchical matrices). The goal is to formalize abstractions for such data structures, to develop Application Programming Interfaces (APIs) that allow the practical development of entire dense and sparse linear algebra libraries specialized for these new data structures, and to develop a theory for optimal performance of blocked algorithms for sequential and parallel architectures, including multi-core architectures.

随着具有多层缓存和/或多个处理核心的处理器的出现，重新检查矩阵应该如何存储在内存中已经成为必要。研究人员研究了分层数据结构在开发线性代数库时如何提高性能并减少编程工作量。特别令人感兴趣的是对未来多核处理器的影响，特别是当内核数量变得很大时。该项目追求线性代数运算算法的理论和实践，以及它们的实现，当矩阵和/或向量被块递归地存储（层次矩阵）。目标是形式化这些数据结构的抽象，开发应用程序编程接口（api），允许为这些新数据结构专门开发整个密集和稀疏线性代数库的实际开发，并为顺序和并行体系结构（包括多核体系结构）开发阻塞算法的最佳性能理论。