Literature survey on low rank approximation of matrices

N Kishore Kumar, J Schneider - Linear and Multilinear Algebra, 2017 - Taylor & Francis
Low rank approximation of matrices has been well studied in literature. Singular value
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …

Fast direct methods for Gaussian processes

S Ambikasaran, D Foreman-Mackey… - IEEE transactions on …, 2015 - ieeexplore.ieee.org
A number of problems in probability and statistics can be addressed using the multivariate
normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a …

Performance and scalability of the block low-rank multifrontal factorization on multicore architectures

PR Amestoy, A Buttari, JY L'excellent… - ACM Transactions on …, 2019 - dl.acm.org
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 …

An efficient multicore implementation of a novel HSS-structured multifrontal solver using randomized sampling

P Ghysels, XS Li, FH Rouet, S Williams… - SIAM Journal on Scientific …, 2016 - SIAM
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian
elimination and exploits low-rank approximation of the resulting dense frontal matrices. We …

A distributed-memory package for dense hierarchically semi-separable matrix computations using randomization

FH Rouet, XS Li, P Ghysels, A Napov - ACM Transactions on …, 2016 - dl.acm.org
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 …

Scaling the “memory wall” for multi-dimensional seismic processing with algebraic compression on cerebras cs-2 systems

H Ltaief, Y Hong, L Wilson, M Jacquelin… - Proceedings of the …, 2023 - dl.acm.org
We exploit the high memory bandwidth of AI-customized Cerebras CS-2 systems for seismic
processing. By leveraging low-rank matrix approximation, we fit memory-hungry seismic …

Hierarchical interpolative factorization for elliptic operators: integral equations

KL Ho, L Ying - arxiv preprint arxiv:1307.2666, 2013 - arxiv.org
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-
IE) associated with elliptic problems in two and three dimensions. This factorization takes the …

Accelerating geostatistical modeling and prediction with mixed-precision computations: A high-productivity approach with parsec

S Abdulah, Q Cao, Y Pei, G Bosilca… - … on Parallel and …, 2021 - ieeexplore.ieee.org
Geostatistical modeling, one of the prime motivating applications for exascale computing, is
a technique for predicting desired quantities from geographically distributed data, based on …

Hierarchical interpolative factorization for elliptic operators: differential equations

KL Ho, L Ying - Communications on Pure and Applied …, 2016 - Wiley Online Library
This paper introduces the hierarchical interpolative factorization for elliptic partial differential
equations (HIF‐DE) in two (2D) and three dimensions (3D). This factorization takes the form …

An immersed boundary method for rigid bodies

B Kallemov, A Bhalla, B Griffith, A Donev - Communications in Applied …, 2016 - msp.org
We develop an immersed boundary (IB) method for modeling flows around fixed or moving
rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes …