A survey of direct methods for sparse linear systems
Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of
them. 1 This informal yet practical definition captures the essence of the goal of direct …
them. 1 This informal yet practical definition captures the essence of the goal of direct …
Performance and scalability of the block low-rank multifrontal factorization on multicore architectures
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 …
rank property that can be efficiently exploited in multifrontal solvers to provide a substantial …
Improving multifrontal methods by means of block low-rank representations
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 …
rank property: well-defined off-diagonal blocks of their Schur complements can be …
Subspace iteration randomization and singular value problems
M Gu - SIAM Journal on Scientific Computing, 2015 - SIAM
A classical problem in matrix computations is the efficient and reliable approximation of a
given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is …
given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is …
[BOOK][B] Efficient numerical methods for non-local operators: H2-matrix compression, algorithms and analysis
S Börm - 2010 - books.google.com
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 …
context of integral equations, elliptic partial differential equations, and control theory. While a …
A fast direct solver for structured linear systems by recursive skeletonization
We present a fast direct solver for structured linear systems based on multilevel matrix
compression. Using the recently developed interpolative decomposition of a low-rank matrix …
compression. Using the recently developed interpolative decomposition of a low-rank matrix …
A distributed-memory package for dense hierarchically semi-separable matrix computations using randomization
We present a distributed-memory library for computations with dense structured matrices. A
matrix is considered structured if its off-diagonal blocks can be approximated by a rank …
matrix is considered structured if its off-diagonal blocks can be approximated by a rank …
Swee** preconditioner for the Helmholtz equation: hierarchical matrix representation
The paper introduces the swee** preconditioner, which is highly efficient for iterative
solutions of the variable‐coefficient Helmholtz equation including very‐high‐frequency …
solutions of the variable‐coefficient Helmholtz equation including very‐high‐frequency …
Real diffusion-weighted MRI enabling true signal averaging and increased diffusion contrast
This project aims to characterize the impact of underlying noise distributions on diffusion-
weighted imaging. The noise floor is a well-known problem for traditional magnitude-based …
weighted imaging. The noise floor is a well-known problem for traditional magnitude-based …