Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form

DOI10.1002/nla.612zbMath1224.65099OpenAlexW2125453344MaRDI QIDQ3011665

Niloufer Mackey, D. Steven Mackey, Christian Mehl, Volker Mehrmann

Publication date: 29 June 2011

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

Full work available at URL: http://eprints.maths.manchester.ac.uk/1109/1/MacMMM08_final.pdf

zbMATH Keywords

eigenvalue problemill-conditioned problemsSchur formpalindromic matrix polynomialpalindromic pencilanti-triangular formpalindromic QR-algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Matrix pencils (15A22)

Related Items (30)

Linearizations of matrix polynomials in Bernstein bases ⋮ On a class of inverse palindromic eigenvalue problem ⋮ Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis ⋮ A note on Sylvester-type equations ⋮ A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems ⋮ Structure preserving stratification of skew-symmetric matrix polynomials ⋮ The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits ⋮ Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method ⋮ Computing the distance to continuous-time instability of quadratic matrix polynomials ⋮ A Framework for Structured Linearizations of Matrix Polynomials in Various Bases ⋮ On the first degree Fejér-Riesz factorization and its applications to \(X+A^{\ast}X^{-1}A=Q\) ⋮ Geometry of matrix polynomial spaces ⋮ The Ehrlich-Aberth method for palindromic matrix polynomials represented in the Dickson basis ⋮ On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations ⋮ The palindromic generalized eigenvalue problem \(A^{*}x=\lambda Ax\): Numerical solution and applications ⋮ The infinite Lanczos method for symmetric nonlinear eigenvalue problems ⋮ Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree ⋮ Structured backward error analysis of linearized structured polynomial eigenvalue problems ⋮ A linear eigenvalue algorithm for the nonlinear eigenvalue problem ⋮ Updating \(\star \)-palindromic quadratic systems with no spill-over ⋮ Palindromic companion forms for matrix polynomials of odd degree ⋮ A bisection method for measuring the distance of a quadratic matrix polynomial to the quadratic matrix polynomials that are singular on the unit circle ⋮ On the simultaneous refinement of the zeros of H-palindromic polynomials ⋮ Pole-swapping algorithms for alternating and palindromic eigenvalue problems ⋮ On inverse eigenvalue problems of quadratic palindromic systems with partially prescribed eigenstructure ⋮ Implicit QR algorithms for palindromic and even eigenvalue problems ⋮ A Fast Algorithm For Fast Train Palindromic Quadratic Eigenvalue Problems ⋮ On the distance to instability of quadratic matrix polynomials ⋮ Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Palindromic Structures ⋮ Palindromic linearization and numerical solution of nonsymmetric algebraic \(T\)-Riccati equations

Cites Work

• Unnamed Item
• Implicit QR algorithms for palindromic and even eigenvalue problems
• Simultaneous equations models in applied search theory
• Some numerical experiments in triangularizing matrices
• The autonomous linear quadratic control problem. Theory and numerical solution
• Polynomial eigenvalue problems with Hamiltonian structure
• On Asymptotic Convergence of Nonsymmetric Jacobi Algorithms
• A Schur method for solving algebraic Riccati equations
• Jacobi-like Algorithms for the Indefinite Generalized Hermitian Eigenvalue Problem
• On the Schur Decomposition of a Matrix for Parallel Computation
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Symmetric Linearizations for Matrix Polynomials
• A Method for Finding Roots of Arbitrary Matrices

This page was built for publication: Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form