Matrices coming from elliptic Partial Differential Equations have been shown to have a low-
rank property that can be efficiently exploited in multifrontal solvers to provide a substantial …

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 …

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 …

In writing this book, I set out to create an accessible introduction to fast multipole methods
(FMMs) and techniques based on integral equation formulations. These are powerful tools …

Matrices possessing a low-rank property arise in numerous scientific applications. This
property can be exploited to provide a substantial reduction of the complexity of their LU or …

Geostatistics represents one of the most challenging classes of scientific applications due to
the desire to incorporate an ever increasing number of geospatial locations to accurately …

In this work, we develop a fast hierarchical solver for solving large, sparse least squares
problems. We build upon the algorithm, spaQR (sparsified QR Gnanasekaran and Darve in …

Due to the well-known computational showstopper of the exact Maximum Likelihood
Estimation (MLE) for large geospatial observations, a variety of approximation methods have …

In this work, we develop a new fast algorithm, spaQR---sparsified QR---for solving large,
sparse linear systems. The key to our approach lies in using low-rank approximations to …

The paper describes a sparse direct solver for the linear systems that arise from the
discretization of an elliptic PDE on a two-dimensional domain. The scheme decomposes the …