@Unpublished{ AmDuSlUç2009.1,

author = {Amestoy, Patrick and Duff, Iain and Slavova, Tzvetomila and Uçar, Bora},

title = "{ON OUT-OF-CORE SOLUTION OF SPARSE LINEAR SYSTEMS FOR SPARSE RIGHT HAND-SIDE VECTORS (Dagstuhl Seminar on Combinatorial Scientific Computing, Dagstuhl, 01/02/2009-06/02/2009)}",

year = {2009},

language = {français},

URL = {http://wiki.stce.rwth-aachen.de/bin/view/CSCDagstuhl/WebHome},

abstract = {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.
}

}