Sparse matrix approximations for multigrid methods

被引：5

作者：

Bolten, Matthias ^{[1
]}

Huckle, Thomas K. ^{[2
]}

Kravvaritis, Christos D. ^{[3
]}

机构：

[1] Univ Kassel, Inst Math, D-34133 Kassel, Germany

[2] Tech Univ Munich, Dept Informat, Boltzmannstr 3, D-85748 Munich, Germany

[3] Univ Athens, Dept Math, Athens 15784, Greece

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 502卷

关键词：

Multigrid; Toeplitz matrices; Generating functions; Sparse matrix approximations; COMPACT FOURIER-ANALYSIS; MULTILEVEL;

D O I：

10.1016/j.laa.2015.11.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the application of sparse matrix approximations for two-grid and V-cycle multigrid methods. Sparse approximate inverses can be used as smoothers, further the Galerkin coarse matrix can be sparsified by sparse approximation techniques. Also the projection can be defined by combining sparse approximation with side conditions related to high frequency components. Numerical results are given, which demonstrate the efficiency and accuracy of the proposed strategies. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：58 / 76

页数：19

共 50 条

[41] REGRESSION WITH SPARSE APPROXIMATIONS OF DATA
Noorzad, Pardis
Sturm, Bob L.
2012 PROCEEDINGS OF THE 20TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), 2012, : 674 - 678
[42] Cascadic multigrid methods
Bornemann, FA
Deuflhard, P
DOMAIN DECOMPOSITION METHODS IN SCIENCES AND ENGINEERING, 1997, : 205 - 212
[43] Iterative Thresholding for Sparse Approximations
Blumensath, Thomas
Davies, Mike E.
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2008, 14 (5-6) : 629 - 654
[44] Computing sparse approximations deterministically
Hofmeister, T
Lefmann, H
LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 240 : 9 - 19
[45] Sparse Approximations for Quaternionic Signals
Quentin Barthélemy
Anthony Larue
Jérôme I. Mars
Advances in Applied Clifford Algebras, 2014, 24 : 383 - 402
[46] Iterative Thresholding for Sparse Approximations
Thomas Blumensath
Mike E. Davies
Journal of Fourier Analysis and Applications, 2008, 14 : 629 - 654
[47] INVERSION OF THE FERMIONIC MATRIX AND MULTIGRID
BARCZYK, T
WIT, R
ACTA PHYSICA POLONICA B, 1991, 22 (07): : 623 - 629
[48] Multigrid for discrete differential forms on sparse grids
Gradinaru, V
Hiptmair, R
COMPUTING, 2003, 71 (01) : 17 - 42
[49] Multigrid for Discrete Differential Forms on Sparse Grids
V. Gradinaru
R. Hiptmair
Computing, 2003, 71 : 17 - 42
[50] Sparse Bayesian Methods for Low-Rank Matrix Estimation
Babacan, S. Derin
Luessi, Martin
Molina, Rafael
Katsaggelos, Aggelos K.
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2012, 60 (08) : 3964 - 3977

← 1 2 3 4 5 →