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 …
decomposition, QR decomposition with column pivoting, rank revealing QR factorization …
Fast direct methods for Gaussian processes
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 …
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
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 …
An efficient multicore implementation of a novel HSS-structured multifrontal solver using randomized sampling
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 …
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
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 …
Scaling the “memory wall” for multi-dimensional seismic processing with algebraic compression on cerebras cs-2 systems
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 …
processing. By leveraging low-rank matrix approximation, we fit memory-hungry seismic …
Hierarchical interpolative factorization for elliptic operators: integral equations
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 …
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
Geostatistical modeling, one of the prime motivating applications for exascale computing, is
a technique for predicting desired quantities from geographically distributed data, based on …
a technique for predicting desired quantities from geographically distributed data, based on …
Hierarchical interpolative factorization for elliptic operators: differential equations
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 …
equations (HIF‐DE) in two (2D) and three dimensions (3D). This factorization takes the form …
An immersed boundary method for rigid bodies
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 …
rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes …