Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods

DOI10.1137/S106482750139220XzbMath1048.65035OpenAlexW2130140345MaRDI QIDQ4442113

Tsung-Min Hwang, Volker Mehrmann, Wen-Wei Lin

Publication date: 20 January 2004

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s106482750139220x

zbMATH Keywords

numerical exampleseigenvectorsinvariant subspacesparse matricesArnoldi methodquadratic eigenvalue problemsquadratic Jacobi-Davidson methoddamped gyroscopic systemsnonequivalence deflation techniqueskew-Hamiltonian/ Hamiltonian pencils

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Invariant subspaces of linear operators (47A15) Matrix pencils (15A22)

Related Items (11)

Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems ⋮ An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems ⋮ Real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices ⋮ A successive quadratic approximations method for nonlinear eigenvalue problems ⋮ Quadratic inverse eigenvalue problem for damped gyroscopic systems ⋮ Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods ⋮ The Jacobi-Davidson method ⋮ A Newton-Type Method with Nonequivalence Deflation for Nonlinear Eigenvalue Problems Arising in Photonic Crystal Modeling ⋮ An iterative method for obtaining the least squares solutions of quadratic inverse eigenvalue problems over generalized Hamiltonian matrix with submatrix constraints ⋮ Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems ⋮ An inverse eigenvalue problem for damped gyroscopic second-order systems

Uses Software

• LAPACK
• JDQR
• ARPACK
• JDQZ

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