A refined Arnoldi type method for large scale eigenvalue problems

DOI10.1007/s13160-012-0090-0zbMath1264.65057OpenAlexW2049348304MaRDI QIDQ1943090

Qiang Niu, Xiang Wang, Lin-Zhang Lu

Publication date: 15 March 2013

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

Full work available at URL: https://doi.org/10.1007/s13160-012-0090-0

zbMATH Keywords

convergenceeigenvalue problemnumerical experimentsRitz valuesRayleigh-Ritz methodeigenpairsArnoldi processHarmonic Ritz values

Mathematics Subject Classification ID

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

Related Items (5)

A refined variant of the inverse-free Krylov subspace method for symmetric generalized eigenvalue problems ⋮ Block subspace projection preconditioned conjugate gradient method in modal structural analysis ⋮ A modified second-order Arnoldi method for solving the quadratic eigenvalue problems ⋮ A new variant of Arnoldi method for approximation of eigenpairs ⋮ A Numerical Method to Solve Nonsymmetric Eigensystems Applied to Dynamics of Turbomachinery

Uses Software

• MatrixMarket
• JDQZ
• Harwell-Boeing sparse matrix collection

Cites Work

• An analogue of the results of Saad and Stewart for harmonic Ritz vectors
• A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems
• Computing interior eigenvalues of large matrices
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• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• Analysis of acceleration strategies for restarted minimal residual methods
• A dynamic thick restarted semi-refined ABLE algorithm for computing a few selected eigentriplets of large nonsymmetric matrices
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• Matrix Algorithms
• Sparse matrix test problems
• The Advantages of Inverted Operators in Rayleigh–Ritz Approximations
• A Large, Sparse, and Indefinite Generalized Eigenvalue Problem from Fluid Mechanics
• An Arnoldi code for computing selected eigenvalues of sparse, real, unsymmetric matrices
• The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• A simpler GMRES
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Harmonic projection methods for large non-symmetric eigenvalue problems
• An invert-free Arnoldi method for computing interior eigenpairs of large matrices
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
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