A Supernodal Cholesky Factorization Algorithm for Shared-Memory Multiprocessors

This paper presents a new left-looking parallel sparse Cholesky fac,torization algorithm for shared-memory MIMD multiprocessors. The algorithm is particularly well-suited for vector supercomputers with multiple processors, such as the Cray Y-MP. The new algorithm uses supernodes in the Cholesky factor to improve performance by reducing indirect addressing and memory traffic. Earlier factorization algorithms have also used supernodes in this manner. The new algorithm, however, also uses supernodes to reduce the number of system synchronization calls, often by an order of magnitude or tnore in practice. Experimental results on a Sequent Balance 8000 and a Cray Y-MP demonstrate the effectiveness of thc new algorithm. On eight processors of a Cray Y-MP, the new routine performs the factorization at rates exceeding one Gflop for several test problems from the Harwell Boeing test collection, none of which are exceedingly large by current standards.