Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems

DOI10.1007/BF01731928zbMath0861.65032OpenAlexW2053245975MaRDI QIDQ1923870

Jane K. Cullum

Publication date: 29 April 1997

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01731928

zbMATH Keywords

convergencenumerical exampleseigenvaluesmatrix eigenvalue problemsArnoldi methodsnonsymmetric matricesLanczo methodsnearly normal matrices

Mathematics Subject Classification ID

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

Related Items (3)

Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems ⋮ Iterative methods for solving \(Ax=b\), GMRES/FOM versus QMR/BiCG ⋮ The effect of non-optimal bases on the convergence of Krylov subspace methods

Uses Software

• Matlab
• eigs
• IRAM

Cites Work

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• Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
• Large-scale complex eigenvalue problems
• A generalized nonsymmetric Lanczos procedure
• Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems
• Hydrodynamic Stability Without Eigenvalues
• Implementation of the GMRES Method Using Householder Transformations
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices

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