Communication-efficient parallel Bruhat decomposition
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.