An upper \(J\)-Hessenberg reduction of a matrix through symplectic Householder transformations

DOI10.1016/j.camwa.2019.02.025zbMath1442.65062arXiv1612.08707OpenAlexW2964048680MaRDI QIDQ2204061

Haithem Ben Kahla, Ahmed Salam

Publication date: 2 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.08707

zbMATH Keywords

indefinite inner productstructure-preserving eigenproblemssymplectic Householder transformations\(SR\) decompositionupper \(J\)-Hessenberg form

Mathematics Subject Classification ID

Factorization of matrices (15A23) Orthogonalization in numerical linear algebra (65F25)

Related Items (1)

A treatment of breakdowns and near breakdowns in a reduction of a matrix to upper \(J\)-Hessenberg form and related topics

Cites Work

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• Optimal symplectic Householder transformations for \(SR\) decomposition
• Error analysis and computational aspects of SR factorization via optimal symplectic Householder transformations
• A Schur decomposition for Hamiltonian matrices
• A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
• Numerical linear algorithms and group theory
• Matrix factorizations for symplectic QR-like methods
• Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms
• Symplectic Householder transformations for a QR-like decomposition, a geometric and algebraic approaches
• On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms
• A symplectic QR like algorithm for the solution of the real algebraic Riccati equation
• The Matrix Eigenvalue Problem

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