Communication-efficient parallel Bruhat decomposition

2026-08-07

AI Summary

This work addresses the high communication and synchronization overhead inherent in Bruhat decomposition under the Bulk-Synchronous Parallel (BSP) model by proposing a novel block-recursive parallel algorithm. For the first time, this approach achieves communication-efficient Bruhat decomposition within the BSP framework, significantly reducing both communication complexity and the number of synchronization steps while preserving numerical stability and matrix structural symmetry. Experimental results demonstrate that the proposed algorithm substantially enhances the scalability of Bruhat decomposition on general-purpose parallel platforms, thereby providing an efficient foundation for large-scale sparse linear algebra computations.

Abstract

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.

Problem

• Bruhat decomposition
• bulk-synchronous parallel
• communication complexity
• synchronization complexity
• block-recursive algorithm

Innovation

• Bruhat decomposition
• bulk-synchronous parallel
• communication-efficient
• block-recursive algorithm
• synchronization complexity