Thick restarting the weighted harmonic Arnoldi algorithm for large interior eigenproblems

DOI10.1080/00207160.2010.489639zbMath1298.65066OpenAlexW1979333447MaRDI QIDQ2995496

Gang Wu, Hong-Xiu Zhong

Publication date: 21 April 2011

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2010.489639

zbMATH Keywords

Arnoldi processweighted Arnoldi processinterior eigenproblemsthick restarting

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Related Items

Deflated and restarted Krylov subspace methods for Sylvester tensor equations ⋮ Some observations on weighted GMRES ⋮ Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem ⋮ Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations ⋮ Generalisation of a quadrilateral duality theorem

Uses Software

• eigs
• JDQR
• JDQZ
• Harwell-Boeing sparse matrix collection

Cites Work

• Unnamed Item
• Unnamed Item
• Computing interior eigenvalues of large matrices
• Restarted weighted full orthogonalization method for shifted linear systems
• Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
• Weighted FOM and GMRES for solving nonsymmetric linear systems
• A note on weighted FOM and GMRES for solving nonsymmetric linear systems
• Balancing sparse matrices for computing eigenvalues
• A harmonic restarted Arnoldi algorithm for calculating eigenvalues and determining multiplicity
• A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigen\-problems
• Balancing a matrix for calculation of eigenvalues and eigenvectors
• Matrix Krylov subspace methods for linear systems with multiple right-hand sides
• Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
• Matrix Algorithms
• On Pre-Conditioning of Matrices
• A Power–Arnoldi algorithm for computing PageRank
• Sparse matrix test problems
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
• Templates for the Solution of Algebraic Eigenvalue Problems
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• GMRES with Deflated Restarting
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
• Harmonic projection methods for large non-symmetric eigenvalue problems

This page was built for publication: Thick restarting the weighted harmonic Arnoldi algorithm for large interior eigenproblems