Structured backward error for palindromic polynomial eigenvalue problems

DOI10.1007/s00211-010-0297-4zbMath1213.65063OpenAlexW1980157955MaRDI QIDQ985700

Wen-Wei Lin, Chern-Shuh Wang, Ren-Cang Li

Publication date: 6 August 2010

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-010-0297-4

zbMATH Keywords

numerical experimentsstructured backward erroreigenpairpalindromic matrix polynomial

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrices over function rings in one or more variables (15A54)

Related Items (8)

A new look at the doubling algorithm for a structured palindromic quadratic eigenvalue problem ⋮ THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM ⋮ Updating \(\star \)-palindromic quadratic systems with no spill-over ⋮ Structured backward error for palindromic polynomial eigenvalue problems. II: Approximate eigentriplets ⋮ Structured backward error analysis for sparse polynomial eigenvalue problems ⋮ On inverse eigenvalue problems of quadratic palindromic systems with partially prescribed eigenstructure ⋮ A Fast Algorithm For Fast Train Palindromic Quadratic Eigenvalue Problems ⋮ Perturbation analysis for palindromic and anti-palindromic nonlinear eigenvalue problems

Cites Work

• On equivalence of pencils from discrete-time and continuous-time control
• Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms
• Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem.
• Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems
• A note on the backward errors for Hermite eigenvalue problems
• Backward error and condition of polynomial eigenvalue problems
• Stability of Structured Hamiltonian Eigensolvers
• The Quadratic Eigenvalue Problem
• Structured Eigenvalue Condition Number and Backward Error of a Class of Polynomial Eigenvalue Problems
• Structure-Preserving Algorithms for Palindromic Quadratic Eigenvalue Problems Arising from Vibration of Fast Trains
• Backward Error and Condition of Structured Linear Systems
• The Strong Stability of Algorithms for Solving Symmetric Linear Systems
• Structured Backward Error and Condition of Generalized Eigenvalue Problems
• Vector Spaces of Linearizations for Matrix Polynomials
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

This page was built for publication: Structured backward error for palindromic polynomial eigenvalue problems