Augmented block Householder Arnoldi method

DOI10.1016/j.laa.2007.12.021zbMath1153.65034OpenAlexW2042163658MaRDI QIDQ952023

James Baglama

Publication date: 6 November 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.12.021

zbMATH Keywords

numerical exampleseigenvectorsaugmentationKrylov subspace methodimplicit shiftsrestarted iterative methodMATLAB codeblock Householder Arnoldi methodlarge sparse nonsymmetric matrixpartial eigenvalue value decomposition

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Symbolic computation and algebraic computation (68W30) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (8)

Nonlinear eigenvalue and frequency response problems in industrial practice ⋮ Accelerating the Sinkhorn-Knopp iteration by Arnoldi-type methods ⋮ A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems ⋮ On the block GMRES method with deflated restarting ⋮ Computing pseudospectra using block implicitly restarted Arnoldi iteration ⋮ Convergence of Arnoldi's method for generalized eigenvalue problems ⋮ Runge--Kutta-Based Explicit Local Time-Stepping Methods for Wave Propagation ⋮ A Block Arnoldi Method for the SPN Equations

Uses Software

• EIGIFP
• irbleigs
• LAPACK
• Matlab
• BLAS
• eigs
• JDQR
• TRLan
• ARPACK
• JDQZ
• Harwell-Boeing sparse matrix collection
• IRAM
• na26
• ABLE
• BLZPACK
• LASO2

Cites Work

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• Restarted block-GMRES with deflation of eigenvalues
• Computing interior eigenvalues of large matrices
• Restarted block Lanczos bidiagonalization methods
• Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling
• Fast Leja points
• Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm
• A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems
• On swapping diagonal blocks in real Schur form
• A block GMRES method augmented with eigenvectors
• Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
• Implicitly Restarted Arnoldi Methods and Subspace Iteration
• A Krylov--Schur Algorithm for Large Eigenproblems
• Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems
• Implementation of the GMRES Method Using Householder Transformations
• A Storage-Efficient $WY$ Representation for Products of Householder Transformations
• LAPACK Users' Guide
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• An Arnoldi code for computing selected eigenvalues of sparse, real, unsymmetric matrices
• A set of level 3 basic linear algebra subprograms
• ARPACK Users' Guide
• IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
• ABLE: An Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• GMRES with Deflated Restarting
• An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
• A Basis-Kernel Representation of Orthogonal Matrices
• On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
• Harmonic projection methods for large non-symmetric eigenvalue problems
• Algorithm 827
• Augmented Implicitly Restarted Lanczos Bidiagonalization Methods
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Dealing with linear dependence during the iterations of the restarted block Lanczos methods

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