Abstract de la publi numéro 10625

We consider efficient solution of sparse linear systems for multiple sparse right hand-side (rhs) vectors, each containing only a single nonzero. We address the problem in the context of out-of-core direct solvers, where the factors are stored on disk. An application which requires solving such a linear system is the computation of the variance matrix (V), or some elements of it, under the standard linear regression model. In this setting, V is the inverse of a symmetric positive-definite matrix, say A. Suppose we are concerned with the computation of the ith diagonal element of V, given a suitable factorization of A. This can be cast as a linear system with A and the ith column of the identity matrix as the rhs vector. The requestd entry can be found by traversing the nodes of the assembly tree from a node to a root node (forward substitution), and then by descending from that root to the starting node (a partial backward substitution). Given a large number of right-hand side vectors, the computations should proceed in epochs---a time slot in which solutions for a reasonable number of rhs vectors take place. An obvious problem then arises: how to partition the rhs vectors into sets in order to optimize system resources. Since we are in the out-of-core context, we aim to minimize the total cost of the factor loading operations. We have successfully modeled the partitioning problem for the application mentioned above in terms of the hypergraph partitioning problem. We will present the model and a few results.