通信高效的并行Bruhat分解
Communication-efficient parallel Bruhat decomposition
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中文总结 AI 辅助
本文针对BSP模型中Bruhat分解的通信与同步复杂度挑战，提出一种新的块递归、通信高效的并行Bruhat分解算法，解决了BSP模型中递归算法表达的问题。
中文摘要 AI 辅助
批量同步并行（BSP）计算模型是一种新兴的通用并行计算范式。Bruhat分解是数值线性代数中的重要方法，它推广了普通LU分解，同时提供了表达选主元的对称结构化方式。过去已针对包括Bruhat分解在内的各类数值线性代数问题开发了块递归算法，但在BSP模型中表达递归算法仍然是一个挑战。本文研究BSP模型中Bruhat分解的通信与同步复杂度，开发了一种新的块递归、通信高效的BSP Bruhat分解算法。
英文摘要
The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. Bruhat decomposition is an important method in numerical linear algebra, generalising ordinary LU decomposition while providing a symmetric structured way of expessing pivoting. Block-recursive algorithms have been developed in the past for various numerical linear algebra problems, including Bruhat decomposition; however, expressing recursive algorithms in the BSP model still remains a challenge. In this paper, we consider the communication and synchronisation complexity of Bruhat decomposition in the BSP model. We develop a new block-recursive, communication-efficient BSP algorithm for Bruhat decomposition.
