@Unpublished{ AmAsBoBuL'We2011.1,
author = {Amestoy, Patrick and Ashcraft, Cleve and Boiteau , Olivier and Buttari, Alfredo and L'Excellent, Jean-Yves and Weisbecker, Clément},
title = "{Grouping variables in Frontal Matrices to improve Low-Rank Approximations in a Multifrontal Solver (International Conference On Preconditioning Techniques For Scientific And Industrial Applications, Preconditioning 2011, Bordeaux, 16/05/2011-18/05/2011)}",
year = {2011},
language = {anglais},
URL = {http://amestoy.perso.enseeiht.fr/doc/weisbecker_precond11.pdf},
keywords = {multifrontal, low-rank, linear algebra, sparse matrix, approximations},
abstract = {Low-rank approximations are commonly used to compress the representation of data
structures. The loss of information induced is often negligible and can be controlled. Although
the dense internal datastructures involved in a multifrontal method, the so-called frontal matrices
or fronts, are full-rank, they can be represented by a set of low-rank matrices. Applying
to our context the notion of geometric clustering used by M. Bebendorf to define hierarchical matrices, we
show that the efficiency of this representation to reduce the complexity of both the factorization
and solve phases strongly depends on how variables are grouped. The proposed approach can be
used either to accelerate the factorization and solution phases or to build a preconditioner, and
aims at exploiting and completing the features of the MUMPS solver for general sparse matrices.
}
}