Foundations and Applications of Hierarchically stored Matrices

随着具有多层高速缓存和/或多个处理核心的处理器的出现，有必要重新检查应该如何将矩阵存储在存储器中。研究人员研究了在开发线性代数库时，分层数据结构如何提高性能并减少编程工作量。特别令人感兴趣的是它对未来多核处理器的影响，特别是当内核数量变得更大时。该项目致力于线性代数运算算法的理论和实践，以及当矩阵和/或向量按块(层次矩阵)递归存储时的实现。目标是形式化这种数据结构的抽象，开发允许实际开发专门用于这些新数据结构的整个密集和稀疏线性代数库的应用编程接口(API)，并开发用于顺序和并行体系结构(包括多核体系结构)的分块算法的优化性能的理论。

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.