A literature survey of low‐rank tensor approximation techniques
L Grasedyck, D Kressner, C Tobler - GAMM‐Mitteilungen, 2013 - Wiley Online Library
During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …
scientific computing to address large‐scale linear and multilinear algebra problems, which …
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 …
[图书][B] Hierarchical matrices: algorithms and analysis
W Hackbusch - 2015 - Springer
Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …
[图书][B] Numerical approximation methods for elliptic boundary value problems: finite and boundary elements
O Steinbach - 2007 - books.google.com
This book presents a unified theory of the Finite Element Method and the Boundary Element
Method for a numerical solution of second order elliptic boundary value problems. This …
Method for a numerical solution of second order elliptic boundary value problems. This …
The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems
This paper presents the adaptive cross approximation (ACA) algorithm to reduce memory
and CPU time overhead in the method of moments (MoM) solution of surface integral …
and CPU time overhead in the method of moments (MoM) solution of surface integral …
Introduction to hierarchical matrices with applications
S Börm, L Grasedyck, W Hackbusch - Engineering analysis with boundary …, 2003 - Elsevier
We give a short introduction to methods for the data-sparse approximation of matrices
resulting from the discretisation of non-local operators occurring in boundary integral …
resulting from the discretisation of non-local operators occurring in boundary integral …
[图书][B] Lecture notes in computational science and engineering
TJ Barth, M Griebel, DE Keyes, RM Nieminen, D Roose… - 2005 - Springer
The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …
models based on differential equations. Initially, the FEniCS Project consisted of two …
[图书][B] The fast solution of boundary integral equations
S Rjasanow, O Steinbach - 2007 - books.google.com
Boundary Element Methods (BEM) play an important role in modern numerical computations
in the applied and engineering sciences. These methods turn out to be powerful tools for …
in the applied and engineering sciences. These methods turn out to be powerful tools for …
On the low-rank approximation by the pivoted Cholesky decomposition
H Harbrecht, M Peters, R Schneider - Applied numerical mathematics, 2012 - Elsevier
The present paper is dedicated to the application of the pivoted Cholesky decomposition to
compute low-rank approximations of dense, positive semi-definite matrices. The resulting …
compute low-rank approximations of dense, positive semi-definite matrices. The resulting …
[图书][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 …