Sparse Matrix Algorithms on Distributed Memory Multiprocessors

将研究分布式内存多处理器上稀疏矩阵问题求解算法的设计、分析和实现。这些并行稀疏矩阵算法的发展应该会对多个科学、计量经济学和工程学科中的大规模计算问题的挑战产生影响。 将研究以下问题： o 谱嵌套剖析算法，用于计算并行有效分解稀疏矩阵的良好排序； o 将计算子任务和给定矩阵映射到分布式内存多处理器中的处理器的算法； o 派系树（一种用于填充矩阵的紧凑表示的数据结构）在几种稀疏矩阵算法中所扮演的角色；以及 o 用于解决分布式内存上最小二乘问题的稀疏正交分解算法的设计多处理器。

The design, analysis, and implementation of algorithms for the solution of sparse matrix problems on distributed memory multiprocessors will be investigated. The development of these parallel sparse matrix algorithms should have an impact of challenging large-scale computational problems in several scientific, econometric, and engineering disciplines. The following are among the problems that will be investigated: o A spectral nested dissection algorithm for computing good orderings for factoring sparse matrices efficiently in parallel, o Algorithms for mapping computational subtasks and the given matrix to the processors in a distributed memory multiprocessor, o The role played by the clique tree, a data structure for the compact representation of filled matrices, in several sparse matrix algorithms, and o The design of sparse orthogonal factorization algorithms for the solution of least-squares problems on distributed memory multiprocessors.