Deflated block Krylov subspace methods for large scale eigenvalue problems

DOI10.1016/j.cam.2009.11.058zbMath1191.65035OpenAlexW1984452975MaRDI QIDQ966072

Qiang Niu, Lin-Zhang Lu

Publication date: 27 April 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.11.058

zbMATH Keywords

numerical examplesorthogonalizationRitz vectorArnoldi-type algorithmRitz valueclustered eigenvaluesdeflated block Krylov subspace methodslarge scale matrix eigenvalue problemsrefined approximate eigenvector

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Uses Software

• irbleigs
• Matlab
• eigs
• JDQR
• ARPACK
• JDQZ
• Harwell-Boeing sparse matrix collection
• IRAM
• ABLE
• lobpcg.m

Cites Work

• Restarted block-GMRES with deflation of eigenvalues
• Block Krylov-Schur method for large symmetric eigenvalue problems
• The block grade of a block Krylov space
• Generalized block Lanczos methods for large unsymmetric eigenproblems
• Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems
• A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems
• Krylov-subspace methods for reduced-order modeling in circuit simulation
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• Matrix Algorithms
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• A Symmetric Band Lanczos Process Based on Coupled Recurrences and Some Applications
• The Lanczos Algorithm With Partial Reorthogonalization
• Sparse matrix test problems
• A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• Preconditioned Gradient-Type Iterative Methods in a Subspace for Partial Generalized Symmetric Eigenvalue Problems
• An Arnoldi code for computing selected eigenvalues of sparse, real, unsymmetric matrices
• ARPACK Users' Guide
• IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
• A Lanczos-type method for multiple starting vectors
• Templates for the Solution of Algebraic Eigenvalue Problems
• Convergence of Restarted Krylov Subspaces to Invariant Subspaces
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
• Convergence of Polynomial Restart Krylov Methods for Eigenvalue Computations
• Convergence Analysis of Krylov Subspace Iterations with Methods from Potential Theory
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
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