面向多核架构的并行分块QR分解
Parallel Tiled QR Factorization for Multicore Architectures
AI总结：
提出一种基于分块和动态任务调度的并行QR分解算法，通过细粒度任务并行和松同步执行，有效隐藏顺序任务，相比LAPACK的BLAS级并行方法显著提升多核性能。
摘要：
随着多核系统在高性能计算领域的不断普及，线性代数算法需要重新设计或开发新算法以利用这些新处理器的架构特性。细粒度并行成为主要需求，并引入了在操作并行执行中松散同步的必要性。本文提出了一种QR分解算法，其中操作可以表示为一系列对数据方块进行操作的小任务。这些任务可以根据它们之间的依赖关系以及计算资源的可用性进行动态调度执行。这可能导致任务的乱序执行，从而完全隐藏分解中固有的顺序任务。与LAPACK的QR分解算法进行了性能比较，后者仅在BLAS操作级别利用并行性。
英文摘要：
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these new processors. Fine grain parallelism becomes a major requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data. These tasks can be dynamically scheduled for execution based on the dependencies among them and on the availability of computational resources. This may result in an out of order execution of the tasks which will completely hide the presence of intrinsically sequential tasks in the factorization. Performance comparisons are presented with the LAPACK algorithm for QR factorization where parallelism can only be exploited at the level of the BLAS operations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
