A Sylvester–Arnoldi type method for the generalized eigenvalue problem with two‐by‐two operator determinants

DOI10.1002/nla.2005zbMath1349.65122OpenAlexW2157529542MaRDI QIDQ5739746

Bor Plestenjak, Karl Meerbergen

Publication date: 19 July 2016

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://lirias.kuleuven.be/handle/123456789/631493

zbMATH Keywords

algorithmsnumerical examplesHopf bifurcationgeneralized eigenvalue problemBartels-Stewart algorithminverse iterationSylvester equationMatlabArnoldi methodlow-rank approximationMathieu's systemtwo-parameter eigenvalue problemseparable boundary value problemssubspace iterationoperator determinantsKrylov-Schur iterations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18) Iterative numerical methods for linear systems (65F10)

Related Items

Solving two-parameter eigenvalue problems using an alternating method ⋮ Numerical methods for nonlinear two-parameter eigenvalue problems ⋮ Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems ⋮ Computing several eigenvalues of nonlinear eigenvalue problems by selection ⋮ Least squares solutions of quadratic inverse eigenvalue problem with partially bisymmetric matrices under prescribed submatrix constraints ⋮ Nonlinearizing Two-parameter Eigenvalue Problems ⋮ Linearizable Eigenvector Nonlinearities

Uses Software

• Matlab
• eigs
• JDQR
• JDQZ
• IRAM
• MultiParEig
• Algorithm 432

Cites Work

• Spectral collocation solutions to multiparameter Mathieu's system
• Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
• Computing elliptic membrane high frequencies by Mathieu and Galerkin methods
• Convergence of inexact inverse iteration with application to preconditioned iterative solvers
• Krylov-subspace methods for the Sylvester equation
• Multiparameter eigenvalue problems and expansion theorems
• A Krylov--Schur Algorithm for Large Eigenproblems
• Separable Boundary‐Value Problems in Physics
• Numerical Methods for Large Eigenvalue Problems
• Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems
• An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
• On the minimal eigenvalue of a positive definite operator determinant
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Charge Singularity at the Corner of a Flat Plate
• A Continuation Method for a Right Definite Two-Parameter Eigenvalue Problem
• A Jacobi--Davidson Type Method for the Two-Parameter Eigenvalue Problem
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]