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A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems

Authors:

Gerard L. G. Sleijpen,

Henk A. Van derAuthors Info & Claims

SIAM Journal on Matrix Analysis and Applications, Volume 17, Issue 2

Pages 401 - 425

https://doi.org/10.1137/S0895479894270427

Published: 01 April 1996 Publication History

Abstract

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.

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Alvermann AHager GFehske H(2023)Orthogonal Layers of Parallelism in Large-Scale Eigenvalue ComputationsACM Transactions on Parallel Computing10.1145/361444410:3(1-31)Online publication date: 22-Sep-2023
https://dl.acm.org/doi/10.1145/3614444
Manin VLang B(2023)Efficient parallel reduction of bandwidth for symmetric matricesParallel Computing10.1016/j.parco.2023.102998115:COnline publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1016/j.parco.2023.102998
Miao CCheng L(2023)On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problemsAdvances in Computational Mathematics10.1007/s10444-023-10078-449:6Online publication date: 24-Oct-2023
https://dl.acm.org/doi/10.1007/s10444-023-10078-4
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A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems

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A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems

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, ...
Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems
Abstract
In this paper we will show how the Jacobi-Davidson iterative method can be used to solve generalized eigenproblems. Similar ideas as for the standard eigenproblem are used, but the projections, that are required to reduce the given problem to a ...
Is Jacobi--Davidson Faster than Davidson?

The Davidson method is a popular technique to compute a few of the smallest (or largest) eigenvalues of a large sparse real symmetric matrix. It is effective when the matrix is nearly diagonal, that is, when the matrix of eigenvectors is close to the ...

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Published In

cover image SIAM Journal on Matrix Analysis and Applications

SIAM Journal on Matrix Analysis and Applications Volume 17, Issue 2

April 1996

237 pages

ISSN:0895-4798

Editor:
G. H. Golub
Stanford Univ., Stanford, CA

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Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 April 1996

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Alvermann AHager GFehske H(2023)Orthogonal Layers of Parallelism in Large-Scale Eigenvalue ComputationsACM Transactions on Parallel Computing10.1145/361444410:3(1-31)Online publication date: 22-Sep-2023
https://dl.acm.org/doi/10.1145/3614444
Manin VLang B(2023)Efficient parallel reduction of bandwidth for symmetric matricesParallel Computing10.1016/j.parco.2023.102998115:COnline publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1016/j.parco.2023.102998
Miao CCheng L(2023)On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problemsAdvances in Computational Mathematics10.1007/s10444-023-10078-449:6Online publication date: 24-Oct-2023
https://dl.acm.org/doi/10.1007/s10444-023-10078-4
Peetz DElbanna A(2021)On the use of multigrid preconditioners for topology optimizationStructural and Multidisciplinary Optimization10.1007/s00158-020-02750-w63:2(835-853)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s00158-020-02750-w
Miao C(2020)On Chebyshev–Davidson Method for Symmetric Generalized Eigenvalue ProblemsJournal of Scientific Computing10.1007/s10915-020-01360-485:3Online publication date: 16-Nov-2020
https://dl.acm.org/doi/10.1007/s10915-020-01360-4
Campos CRoman J(2019)A polynomial Jacobi–Davidson solver with support for non-monomial bases and deflationBIT10.1007/s10543-019-00778-z60:2(295-318)Online publication date: 29-Aug-2019
https://dl.acm.org/doi/10.1007/s10543-019-00778-z
Accaputo GDerlet PArbenz P(2019)Solving Large-Scale Interior Eigenvalue Problems to Investigate the Vibrational Properties of the Boson Peak Regime in Amorphous MaterialsHigh Performance Computing in Science and Engineering10.1007/978-3-030-67077-1_5(80-98)Online publication date: 20-May-2019
https://dl.acm.org/doi/10.1007/978-3-030-67077-1_5
Lee DHoshi TSogabe TMiyatake YZhang S(2018)Solution of the k-th eigenvalue problem in large-scale electronic structure calculationsJournal of Computational Physics10.1016/j.jcp.2018.06.002371:C(618-632)Online publication date: 15-Oct-2018
https://dl.acm.org/doi/10.1016/j.jcp.2018.06.002
Yang LSun YGong F(2018)The inexact residual iteration method for quadratic eigenvalue problem and the analysis of convergenceJournal of Computational and Applied Mathematics10.1016/j.cam.2017.10.003332:C(45-55)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1016/j.cam.2017.10.003
Zhao T(2018)A Convergence Analysis of the Inexact Simplified Jacobi---Davidson Algorithm for Polynomial Eigenvalue ProblemsJournal of Scientific Computing10.1007/s10915-017-0582-975:3(1207-1228)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1007/s10915-017-0582-9
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