The multifrontal method and paging in sparse Cholesky factorization

Abstract

In this paper, we show that the multifrontal method can have significant advantage over the conventional sparse column-Cholesky scheme on a paged virtual memory system. A more than tenfold reduction in paging activities can be achieved, which saves as much as 20 percent in factorization time. We also introduce a hybrid sparse factorization method, which uses a mixture of column-Cholesky and submatrix-Cholesky operations. By switching to the use of frontal matrices from column-Cholesky operations at appropriate columns, we demonstrate that the proposed hybrid scheme has an advantage over the sparse column-Cholesky method in reducing paging activities and over the multifrontal method in its adaptability to the amount of available working storage.