Alternative correction equations in the Jacobi-Davidson method

DOI<235::AID-NLA166>3.0.CO;2-8 10.1002/(SICI)1099-1506(199904/05)6:3<235::AID-NLA166>3.0.CO;2-8zbMath0983.65047OpenAlexW1493603347MaRDI QIDQ2760355

Gerard L. G. Sleijpen, Menno Genseberger

Publication date: 19 December 2001

Full work available at URL: https://doi.org/10.1002/(sici)1099-1506(199904/05)6:3<235::aid-nla166>3.0.co;2-8

zbMATH Keywords

algorithmconvergencenumerical experimentsinvariant subspacedeflationKrylov subspace methodJacobi-Davidson methodRayleigh-Ritz procedurenonsymmetric eigenvalue probleminexact truncated RQ method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Related Items (10)

Computing eigenpairs in augmented Krylov subspace produced by Jacobi-Davidson correction equation ⋮ The least squares and line search in extracting eigenpairs in Jacobi-Davidson method ⋮ On the subspace projected approximate matrix method. ⋮ On the correction equation of the Jacobi-Davidson method ⋮ An integrated Davidson and multigrid solution approach for very large scale symmetric eigenvalue problems ⋮ Behavior of the correction equations in the Jacobi-Davidson method ⋮ Computing eigenpairs of Hermitian matrices in augmented Krylov subspace produced by Rayleigh quotient iterations ⋮ Rayleigh quotient minimization method for symmetric eigenvalue problems ⋮ New methods for calculations of the lowest eigenvalues of the real symmetric generalized eigenvalue problem ⋮ Filtered Krylov-like sequence method for symmetric eigenvalue problems

Uses Software

• VLUGR3
• JDQR

Cites Work

• Unnamed Item
• VLUGR3: A vectorizable adaptive grid solver for PDEs in 3D. I: Algorithmic aspects and applications
• Robust preconditioning of large, sparse, symmetric eigenvalue problems
• Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
• Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices
• A Truncated RQ Iteration for Large Scale Eigenvalue Calculations
• Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
• Truncation Strategies for Optimal Krylov Subspace Methods
• Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
• Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations
• Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
• GMRESR: a family of nested GMRES methods
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• On restarting the Arnoldi method for large nonsymmetric eigenvalue problems

This page was built for publication: Alternative correction equations in the Jacobi-Davidson method