Abstract-To exploit the potential of multicore architectures, recent dense linear algebra libraries have used tile algorithms, which consist in scheduling a Directed Acyclic Graph (DAG) of tasks of fine granularity where nodes represent tasks, either panel factorization or update of a block-column, and edges represent dependencies among them. Although past approaches already achieve high performance on moderate and large square matrices, their way of processing a panel in sequence leads to limited performance when factorizing tall and skinny matrices or small square matrices. We present a new fully asynchronous method for computing a QR factorization on sharedmemory multicore architectures that overcomes this bottleneck. Our contribution is to adapt an existing algorithm that performs a panel factorization in parallel (named CommunicationAvoiding QR and initially designed for distributed-memory machines), to the context of tile algorithms using asynchronous computations. An experimental study shows significant improvement (up to almost 10 times faster) compared to stateof-the-art approaches. We aim to eventually incorporate this work into the Parallel Linear Algebra for Scalable Multi-core Architectures (PLASMA) library.
Hadri et al. REF present a QRD method for shared-memory multicore architectures and modified an existing algorithm to perform panel factorization in parallel.
Tile QR factorization with parallel panel processing for multicore architectures
2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS)
2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS)
Computer Science