On linearizations of the quadratic two-parameter eigenvalue problem

DOI10.1016/j.laa.2011.07.026zbMath1245.65042OpenAlexW2132960315MaRDI QIDQ413520

Andrej Muhič, Michiel E. Hochstenbach, Bor Plestenjak

Publication date: 7 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.laa.2011.07.026

zbMATH Keywords

linearizationnumerical experimentsquadratic two-parameter eigenvalue problemtwo-parameter eigenvalue problem

Mathematics Subject Classification ID

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

Related Items (15)

Bounds for the spectrum of a two parameter matrix eigenvalue problem ⋮ Numerical methods for nonlinear two-parameter eigenvalue problems ⋮ Computing the Signed Distance Between Overlapping Ellipsoids ⋮ Vector space of linearizations for the quadratic two-parameter matrix polynomial ⋮ On the singular two-parameter eigenvalue problem. II ⋮ Conservation of the number of the eigenvalues of two-parameter matrix problems in bounded domains under perturbations ⋮ Asymptotic boundary conditions for the analysis of hydrodynamic stability of flows in regions with open boundaries ⋮ On quasiregular spectrum of matrix pencils ⋮ A method for computing all values \({\lambda}\) such that \(A + {\lambda}B\) has a multiple eigenvalue ⋮ Roots of Bivariate Polynomial Systems via Determinantal Representations ⋮ Fiber product homotopy method for multiparameter eigenvalue problems ⋮ The homotopy method for the complete solution of quadratic two-parameter eigenvalue problems ⋮ Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation ⋮ Two complementary block Macaulay matrix algorithms to solve multiparameter eigenvalue problems ⋮ Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems

Uses Software

• MultiParEig

Cites Work

• Multiparameter eigenvalue problems. Volume I: Matrices and compact operators
• Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
• Complete description of determinantal representations of smooth irreducible curves
• On the quadratic two-parameter eigenvalue problem and its linearization
• Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations
• The Quadratic Eigenvalue Problem
• Numerical methods for large eigenvalue problems
• On the singular two-parameter eigenvalue problem
• A Jacobi--Davidson Type Method for the Two-Parameter Eigenvalue Problem
• Using Algebraic Geometry
• On the Pseudospectra of Matrix Polynomials
• Vector Spaces of Linearizations for Matrix Polynomials

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