Sparse supernodal solver using block low-rank compression: Design, performance and analysis
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 …
to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver …
An algebraic sparsified nested dissection algorithm using low-rank approximations
We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite
linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection …
linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection …
Hierarchical orthogonal factorization: Sparse least squares problems
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 …
problems. We build upon the algorithm, spaQR (sparsified QR Gnanasekaran and Darve in …
A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel.
The solver is based on a modification of the LoRaSp method, but employs a deferred …
The solver is based on a modification of the LoRaSp method, but employs a deferred …
Recursively preconditioned hierarchical interpolative factorization for elliptic partial differential equations
The hierarchical interpolative factorization for elliptic partial differential equations is a fast
algorithm for approximate sparse matrix inversion in linear or quasilinear time. Its accuracy …
algorithm for approximate sparse matrix inversion in linear or quasilinear time. Its accuracy …
Sparse supernodal solver using block low-rank compression
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 …
to reduce the memory footprint and/or the time-to-solution of the sparse supernodal solver …
Hierarchical orthogonal factorization: Sparse square matrices
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 …
sparse linear systems. The key to our approach lies in using low-rank approximations to …
Sparse hierarchical preconditioners using piecewise smooth approximations of eigenvectors
B Klockiewicz, E Darve - SIAM Journal on Scientific Computing, 2020 - SIAM
When solving linear systems arising from PDE discretizations, iterative methods (such as
conjugate gradient (CG), GMRES, or MINRES) are often the only practical choice. To …
conjugate gradient (CG), GMRES, or MINRES) are often the only practical choice. To …
Second‐order accurate hierarchical approximate factorizations for solving sparse linear systems
We describe a second‐order accurate approach to sparsifying the off‐diagonal matrix blocks
in the hierarchical approximate factorization methods for solving sparse linear systems …
in the hierarchical approximate factorization methods for solving sparse linear systems …
On the use of low-rank arithmetic to reduce the complexity of parallel sparse linear solvers based on direct factorization techniques
G Pichon - 2018 - inria.hal.science
Solving sparse linear systems is a problem that arises in many scientific applications, and
sparse direct solvers are a time consuming and key kernel for those applications and for …
sparse direct solvers are a time consuming and key kernel for those applications and for …