Parallel sparse Cholesky factorization on a shared memory multiprocessor

Parallel implementations of Cholesky factorization for sparse symmetric positive definite matrices are considered on a shared memory multiprocessor computer. Two column-oriented schemes, known as the column-Cholesky algorithm and the fan-in algorithm, along with enhancements of each, are implemented and discussed. High parallel efficiency of the column-Cholesky algorithm and its enhancement is demonstrated for test problems. A detailed investigation of the performance of the fan-in algorithm and its enhancement, the compute-ahead fan-in algorithm, is made to study the effects of overhead associated with the fan-in based schemes.