A generalized nonsymmetric Lanczos procedure

DOI10.1016/0010-4655(89)90146-XzbMath0798.65050MaRDI QIDQ1330632

Wolfgang Kerner, Jane K. Cullum, Ralph A. Willoughby

Publication date: 30 October 1994

Published in: Computer Physics Communications (Search for Journal in Brave)

zbMATH Keywords

eigenvectorsmagnetohydrodynamicsinterior eigenvaluesnonsymmetric Lanczos proceduregeneralized nonsymmetric eigenvalue problemsRayleigh quotient-inverse iterationshift and invert strategy

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items (14)

The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization ⋮ Lanczos-type variants of the COCR method for complex nonsymmetric linear systems ⋮ Some aspects of finite element calculations applied to ULF magnetospheric cavity waves ⋮ Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems ⋮ Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems ⋮ A projection method for generalized eigenvalue problems using numerical integration. ⋮ Eigenmode solution of 2-D and 3-D electromagnetic cavities containing absorbing materials using the Jacobi-Davidson algorithm ⋮ An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems ⋮ The Lanczos algorithm and complex Gauss quadrature ⋮ A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms ⋮ Krylov space methods on state-space control models ⋮ Generalized eigenvalue problems: Lanczos algorithm with a recursive partitioning method ⋮ Eigenvalue computation in the 20th century ⋮ The nonsymmetric Lanczos algorithm and controllability

Uses Software

• EISPACK
• LINPACK

Cites Work

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• Complex shift and invert strategies for real matrices
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
• Matrix eigensystem routines. EISPACK guide extension
• Large-scale complex eigenvalue problems
• Finite-element semi-discretization of linearized compressible and resistive MHD
• Matrix eigensystem routines - EISPACK guide
• Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• Analytic theory of stable resistive magnetohydrodynamic modes
• How to Implement the Spectral Transformation
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• The Advantages of Inverted Operators in Rayleigh–Ritz Approximations
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices
• Estimates for Some Computational Techniques in Linear Algebra
• Computing Invariant Subspaces of a General Matrix when the Eigensystem is Poorly Conditioned

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