Lanczos algorithms and field of value rotations for symmetric matrix pencils

DOI10.1016/0024-3795(87)90132-7zbMath0623.65047OpenAlexW1968767189MaRDI QIDQ1091760

Thomas Ericsson, Axel Ruhe

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90132-7

zbMATH Keywords

eigensolutionArnoldi algorithmspectral transformationIterative algorithmsnonsymmetric Lanczos algorithmsymmetric Lanczos algorithmindefinite pencilssymmetric pencils of matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix pencils (15A22)

Related Items (6)

Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils ⋮ Variational and numerical methods for symmetric matrix pencils ⋮ Methods and algorithms of solving spectral problems for polynomial and rational matrices ⋮ Matrix pencils: Theory, applications, and numerical methods ⋮ Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem ⋮ Numerical methods and questions in the organization of calculus. XII. Transl. from the Russian

Cites Work

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• Matrices and indefinite scalar products
• 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
• Perturbation bounds for the definite generalized eigenvalue problem
• A recurring theorem about pairs of quadratic forms and extensions: A survey
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• A Stable Generalized Eigenvalue Problem
• Algorithms for the Nonlinear Eigenvalue Problem

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