Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

The numerical treatment of partial differential equations splits into two different parts. The
first part are the discretisation methods and their analysis. This led to the author's …

Matrices coming from elliptic partial differential equations have been shown to have a low-
rank property: well-defined off-diagonal blocks of their Schur complements can be …

Hierarchical matrices present an efficient way of treating dense matrices that arise in the
context of integral equations, elliptic partial differential equations, and control theory. While a …

In this paper we develop a fast direct solver for large discretized linear systems using the
supernodal multifrontal method together with low-rank approximations. For linear systems …

Bei der Diskretisierung von Randwertaufgaben und Integralgleichungen entstehen große,
eventuell auch voll besetzte Matrizen. Es wird eine neuartige Methode dargestellt, die es …

Hierarchical matrices provide a data-sparse way to approximate fully populated matrices.
The two basic steps in the construction of an\mathcal H-matrix are (a) the hierarchical …

We investigate the use of low-rank approximations to reduce the cost of sparsedirect
multifrontal solvers. Among the different matrix representations that havebeen proposed to …

A version of the H H-LU factorization is introduced, based on the individual computational
tasks occurring during the block-wise H H-LU factorization. The dependencies between …

This paper presents two approaches using a Block Low-Rank (BLR) compression technique
to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver …