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
收藏
页码：3307 / 3326
页数：20
相关论文
共 50 条
  • [1] KRYLOV SUBSPACE METHODS FOR LINEAR SYSTEMS WITH TENSOR PRODUCT STRUCTURE
    Kressner, Daniel
    Tobler, Christine
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2010, 31 (04) : 1688 - 1714
  • [2] Galerkin projection methods for solving multiple linear systems
    Chan, Tony F.
    Ng, Michael K.
    SIAM Journal on Scientific Computing, 21 (03): : 836 - 850
  • [3] Galerkin projection methods for solving multiple linear systems
    Chan, TF
    Ng, MK
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 21 (03): : 836 - 850
  • [4] Tensor Product And Linear Error Block Codes
    Belabssir, Soukaina
    Sahlal, Nadir
    IAENG International Journal of Applied Mathematics, 2021, 51 (02):
  • [5] Projection methods for linear systems
    Brezinski, C
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 77 (1-2) : 35 - 51
  • [6] Stochastic Galerkin Methods for Linear Stability Analysis of Systems with Parametric Uncertainty
    Sousedik, Bedrich
    Lee, Kookjin
    SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2022, 10 (03): : 1101 - 1129
  • [7] A projection method to solve linear systems in tensor format
    Ballani, Jonas
    Grasedyck, Lars
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2013, 20 (01) : 27 - 43
  • [8] DFOM algorithm and error analysis for projection methods for solving singular linear system
    Zhou, JY
    Wei, YM
    APPLIED MATHEMATICS AND COMPUTATION, 2004, 157 (02) : 313 - 329
  • [9] AN ERROR ANALYSIS FOR RATIONAL GALERKIN PROJECTION APPLIED TO THE SYLVESTER EQUATION
    Beckermann, Bernhard
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2011, 49 (06) : 2430 - 2450
  • [10] Block Projection Methods for Linear Systems
    C. Brezinski
    M. Redivo Zaglia
    Numerical Algorithms, 2002, 29 : 33 - 43
12345