分布式并行机上稠密线性方程组的直接解法

Direct Solutions of Dense Linear Equations on Distributed Parallel Computers

本文综合介绍稠密线性方程组的几种直接解法，介绍常用的处理机与矩阵元素间的映射方案并详细给出环绕映射的分配方案。最后从理论和实验两方面介绍各种分配方案间的性能比较。从比较发现：环绕映射性能最优且可扩展性最好。

In this paper,we give a comprehensive introduction of several directsolutions of dense linear equations and common mapping schemes between matrix ele-ments and processors. Additionally we descricbe the torus-mapping in detail. Finally,wecompare the different performances among various mapping methods from both theoreti-cal and experimental viewpoints. The conclusion is:the torus-mapping has the best per-formance and scalability.