AN ERROR ANALYSIS OF GALERKIN PROJECTION METHODS FOR LINEAR SYSTEMS WITH TENSOR PRODUCT STRUCTURE

被引：9

作者：

Beckermann, Bernhard ^{[1
]}

Kressner, Daniel ^{[2
]}

Tobler, Christine ^{[2
]}

机构：

[1] UST Lille, UFR Math M3, Lab Painleve UMR ANO EDP 8524, F-59655 Villeneuve Dascq, France

[2] EPF Lausanne, MATHICSE, ANCHP, CH-1015 Lausanne, Switzerland

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 06期

关键词：

linear system; Kronecker product structure; Sylvester equation; tensor projection; Galerkin projection; rational Krylov subspaces; KRYLOV SUBSPACE METHODS; LYAPUNOV; APPROXIMATION; EQUATIONS;

D O I：

10.1137/120900204

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Galerkin projection based on tensor products of rational Krylov subspaces. The results can be used to optimize the choice of shifts for these methods. Numerical experiments demonstrate that the convergence rates predicted by our bounds appear to be sharp.

引用

页码：3307 / 3326

页数：20

共 50 条

[41] ASYMPTOTIC ERROR ANALYSIS OF PROJECTION AND MODIFIED PROJECTION METHODS FOR NONLINEAR INTEGRAL EQUATIONS
Kulkarni, Rekha P.
Nidhin, T. J.
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2015, 27 (01) : 67 - 101
[42] TENSOR PRODUCT ANALYSIS OF ALTERNATING DIRECTION IMPLICIT METHODS
LYNCH, RE
RICE, JR
THOMAS, DH
JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1965, 13 (04): : 995 - &
[43] Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
Grasedyck, L
COMPUTING, 2004, 72 (3-4) : 247 - 265
[44] Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure
L. Grasedyck
Computing, 2004, 72 : 247 - 265
[45] Analysis of projection methods for solving linear systems with multiple right-hand sides
Chan, TF
Wan, WL
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1997, 18 (06): : 1698 - 1721
[46] New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor
Qingguo Hong
Jun Hu
Limin Ma
Jinchao Xu
Numerische Mathematik, 2021, 149 : 645 - 678
[47] Asymptotically exact discontinuous Galerkin error estimates for linear symmetric hyperbolic systems
Adjerid, Slimane
Weinhart, Thomas
APPLIED NUMERICAL MATHEMATICS, 2014, 76 : 101 - 131
[48] New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor
Hong, Qingguo
Hu, Jun
Ma, Limin
Xu, Jinchao
NUMERISCHE MATHEMATIK, 2021, 149 (03) : 645 - 678
[49] OPTIMAL ERROR ESTIMATES OF THE SEMIDISCRETE CENTRAL DISCONTINUOUS GALERKIN METHODS FOR LINEAR HYPERBOLIC EQUATIONS
Liu, Yong
Shu, Chi-Wang
Zhang, Mengping
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (01) : 520 - 541
[50] Error Estimates of Spectral Galerkin Methods for a Linear Fractional Reaction-Diffusion Equation
Zhang, Zhongqiang
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 78 (02) : 1087 - 1110

← 1 2 3 4 5 →