Variational and numerical methods for symmetric matrix pencils

DOI10.1017/S0004972700028732zbMath0714.65042MaRDI QIDQ3200474

Qiang Ye, Peter Lancaster

Publication date: 1991

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

perturbation theoryeigenvaluesvariational methodsminimax principlesRayleigh quotient iterationindefinite matricesLanczos algorithmsHermitian matrix pencilRitz projections

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Matrix pencils (15A22)

Related Items

Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils, A Jacobi-Davidson type method for computing real eigenvalues of the quadratic eigenvalue problem, An indefinite variant of LOBPCG for definite matrix pencils, Preconditioned gradient iterations for the eigenproblem of definite matrix pairs, Rayleigh quotient algorithms for nonsymmetric matrix pencils, Singular numbers of contractions in spaces with an indefinite metric and Yamamoto's theorem

Cites Work

• Unnamed Item
• A generalized Rayleigh quotient iteration for lambda-matrices
• Simultaneous equations models in applied search theory
• Lanczos algorithms and field of value rotations for symmetric matrix pencils
• Inverse spectral problems for linear and quadratic matrix pencils
• Perturbation bounds for the definite generalized eigenvalue problem
• The eigenstructure of an arbitrary polynomial matrix: Computational aspects
• Some variational principles for a nonlinear eigenvalue problem
• A minimax theory for overdamped systems
• Localization Criteria and Containment for Rayleigh Quotient Iteration
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices
• Canonical forms for symplectic and Hamiltonian matrices
• Minimaxprinzipe zur Bestimmung der Eigenwerte $J$-nichtnegativer Operatoren.
• A Stable Generalized Eigenvalue Problem
• Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues
• Estimates for Some Computational Techniques in Linear Algebra
• Iterative procedures related to relaxation methods for eigenvalue problems