Parallel Numerical Algorithms and Software

问题将从广泛的数值分析中进行研究，并将确定在多大程度上可以为并行计算机导出快速稳定的算法。将考虑两类并行架构：(1)共享内存多处理器（CRAY-X-MP, CRAY-2, ETA-10, Encore Multimax）。(2)分布式内存消息传递架构（NCUBE, Cyberplus）。研究的目标是：(1)确定各种先进架构可在多大程度上加快计算速度；(2)获得可用于推导适用于高速并行处理的高效稳定算法的通用设计技术；(3)开发在并行架构上有效实现这些算法的鲁棒代码。迄今为止进行的研究已经导致发现了一种设计技术，用于并行化求解大型稀疏线性方程组的一类迭代方法。对于具有内存层次结构的共享内存机器和消息传递机器，已经获得了高效的并行算法，并且比现有算法更快。8722260

Problems will be studied from a broad spectrum of numerical analysis and it will be determined to what extent fast stable algorithms can be derived for parallel computers. Two categories of parallel architectures will be considered: (1) Shared memory multiprocessors (CRAY-X-MP, CRAY-2, ETA-10, Encore Multimax). (2) Distributed memory message passing architectures (NCUBE, Cyberplus). The goals of the research are: (1) To determine the extent to which various advanced architectures can be utilized to speed up computations, (2) To obtain general design techniques that can be used to derive efficient stable algorithms suitable for high sped parallel processing, and (3) To develop robust codes which efficiently implement these algorithms on parallel architectures. The research conducted to date has resulted in the discovery of a design technique for parallelizing a class of iterative methods for solving large sparse linear systems of equations. Efficient parallel algorithms for shared memory machines with memory hierarchy and for message passing machines have been obtained and are faster than previously existing algorithms. 8722260