Structure-Preserving Algorithms for Palindromic Quadratic Eigenvalue Problems Arising from Vibration of Fast Trains

DOI10.1137/080713550zbMath1180.65043OpenAlexW2116581037MaRDI QIDQ3642848

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Publication date: 6 November 2009

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/9d10071ac0c28f94517bef7738f282c11d72de9c

zbMATH Keywords

numerical example palindromic quadratic eigenvalue problem \(\top\)-skew-Hamiltonian pencil \(\top\)-symplectic pencil vibration of fast trains

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (18)

On a class of inverse palindromic eigenvalue problem ⋮ A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem ⋮ The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits ⋮ Solving large-scale nonlinear matrix equations by doubling ⋮ Structure-preserving methods for computing complex band structures of three dimensional photonic crystals ⋮ The palindromic generalized eigenvalue problem \(A^{*}x=\lambda Ax\): Numerical solution and applications ⋮ Computing the full spectrum of large sparse palindromic quadratic eigenvalue problems arising from surface Green's function calculations ⋮ Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree ⋮ Palindromic companion forms for matrix polynomials of odd degree ⋮ Structured backward error for palindromic polynomial eigenvalue problems. II: Approximate eigentriplets ⋮ A semiorthogonal generalized Arnoldi method and its variations for quadratic eigenvalue problems ⋮ A framework for analyzing nonlinear eigenproblems and parametrized linear systems ⋮ Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in leaky surface wave propagation ⋮ Palindromic linearizations of palindromic matrix polynomials of odd degree obtained from Fiedler-like pencils ⋮ Structured backward error for palindromic polynomial eigenvalue problems ⋮ Constructing strong \(\ell\)-ifications from dual minimal bases ⋮ A Fast Algorithm For Fast Train Palindromic Quadratic Eigenvalue Problems ⋮ Canonical forms for congruence of matrices and \(T\)-palindromic matrix pencils: a tribute to H. W. Turnbull and A. C. Aitken

Uses Software

ARPACK

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