On evaluating parallel sparse Cholesky factorizations

Though many parallel implementations of sparse Cholesky factorization with the experimental results accompanied have been proposed, it seems hard to evaluate the performance of these factorization methods theoretically because of the irregular structure of sparse matrices. This paper is an attempt to such research. On the basis of the criteria of parallel computation and communication time, we successfully evaluate four widely adopted Cholesky factorization methods, including column-Cholesky, row-Cholesky, submatrix-Cholesky and multifrontal. The results show that the multifrontal method is superior to the others.