Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils

DOI10.1016/0024-3795(93)90212-7zbMath0771.65017OpenAlexW2118887832MaRDI QIDQ2365722

Qiang Ye, Peter Lancaster

Publication date: 29 June 1993

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

Full work available at URL: https://doi.org/10.1016/0024-3795(93)90212-7

zbMATH Keywords

convergenceeigenvaluenumerical examplesKrylov subspacesRayleigh-Ritz methodsLanczos algorithmssymmetric matrix pencils

Mathematics Subject Classification ID

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

Related Items

A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms, Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems

Cites Work

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• Matrices and indefinite scalar products
• Lanczos algorithms and field of value rotations for symmetric matrix pencils
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Perturbation bounds for the definite generalized eigenvalue problem
• Use of indefinite pencils for computing damped natural modes
• Variational and numerical methods for symmetric matrix pencils
• Iterative Solution of Indefinite Symmetric Linear Systems by Methods Using Orthogonal Polynomials over Two Disjoint Intervals
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• A Convergence Analysis for Nonsymmetric Lanczos Algorithms
• Overdamped and Gyroscopic Vibrating Systems
• Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum
• Estimates for Some Computational Techniques in Linear Algebra