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 …

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 …

[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 …

[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 …

The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems

K Zhao, MN Vouvakis, JF Lee - IEEE transactions on …, 2005 - ieeexplore.ieee.org
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 …

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 …

[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 …

[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 …

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 …

[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 …