A Jacobi-Davidson iteration method for linear eigenvalue problems

被引：3
|
作者：
Sleijpen, GLG
VanderVorst, HA
机构：
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1996年 / 17卷 / 02期
关键词：
eigenvalues and eigenvectors; Davidson's method; Jacobi iterations; harmonic Ritz values;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we propose a new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi's approach, combined with Davidson's method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also propose a variant of the new method that may be useful for the computation of nonextremal eigenvalues as well.
引用
收藏
页码：401 / 425
页数：25
相关论文
共 50 条
  • [1] A Jacobi-Davidson iteration method for linear eigenvalue problems
    Sleijpen, GLG
    Van der Vorst, HA
    [J]. SIAM REVIEW, 2000, 42 (02) : 267 - 293
  • [2] A Jacobi-Davidson method for solving complex symmetric eigenvalue problems
    Arbenz, P
    Hochstenbach, ME
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2004, 25 (05): : 1655 - 1673
  • [3] Jacobi-Davidson method for the second order fractional eigenvalue problems
    He, Ying
    Zuo, Qian
    [J]. CHAOS SOLITONS & FRACTALS, 2021, 143
  • [4] Jacobi-Davidson methods for cubic eigenvalue problems
    Hwang, TM
    Lin, WW
    Liu, JL
    Wang, WC
    [J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2005, 12 (07) : 605 - 624
  • [5] Preconditioned inexact Jacobi-Davidson method for large symmetric eigenvalue problems
    Miao, Hong-Yi
    Wang, Li
    [J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2020, 39 (03):
  • [6] Parallel Jacobi-Davidson for solving generalized eigenvalue problems
    Nool, M
    van der Ploeg, A
    [J]. VECTOR AND PARALLEL PROCESSING - VECPAR'98, 1999, 1573 : 58 - 70
  • [7] A Jacobi-Davidson type method for the product eigenvalue problem
    Hochstenbach, Michiel E.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 212 (01) : 46 - 62
  • [8] ON THE CONVERGENCE OF A TWO-LEVEL PRECONDITIONED JACOBI-DAVIDSON METHOD FOR EIGENVALUE PROBLEMS
    Wang, Wei
    Xu, Xuejun
    [J]. MATHEMATICS OF COMPUTATION, 2019, 88 (319) : 2295 - 2324
  • [9] Jacobi-Davidson methods for generalized MHD-eigenvalue problems
    Booten, A
    Fokkema, D
    Sleijpen, G
    VanderVorst, H
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1996, 76 : 131 - 134
  • [10] A MULTILEVEL JACOBI-DAVIDSON METHOD FOR POLYNOMIAL PDE EIGENVALUE PROBLEMS ARISING IN PLASMA PHYSICS
    Hochbruck, Marlis
    Loechel, Dominik
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (06): : 3151 - 3169
12345