一类多核并行分块线性代数算法
A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures
摘要：
随着多核系统在高性能计算领域的不断发展，必须重新制定线性代数算法或开发新算法，以便利用这些新处理器上的架构功能。细粒度并行性成为一个主要需求，并在操作的并行执行中引入了松同步的必要性。本文提出了一种Cholesky，LU和QR分解的算法，其中的操作可以表示为一系列的小任务，操作的方块数据。这些任务可以根据它们之间的依赖关系和计算资源的可用性来动态调度执行。这可能导致任务的乱序执行，这将完全隐藏因式分解中固有顺序任务的存在。性能比较与LAPACK算法的并行性只能利用在BLAS操作和供应商实现的水平。
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 Cholesky, LU and 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 algorithms where parallelism can only be exploited at the level of the BLAS operations and vendor implementations.
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