Short recurrences for computing extended Krylov bases for Hermitian and unitary matrices

DOI10.1007/s00211-014-0692-3zbMath1330.65063OpenAlexW2007807079MaRDI QIDQ495542

Clara Mertens, Raf Vandebril

Publication date: 14 September 2015

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

Full work available at URL: https://lirias.kuleuven.be/handle/123456789/434811

zbMATH Keywords

algorithmHermitian matricesorthogonal basisunitary matrices\(QR\) factorizationbounded matricesextended Hessenberg formextended Krylov subspacetwo term recurrence relations

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Hermitian, skew-Hermitian, and related matrices (15B57) Orthogonalization in numerical linear algebra (65F25) Orthogonal matrices (15B10)

Related Items (4)

A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching ⋮ Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations ⋮ Orthogonal rational functions on the unit circle with prescribed poles not on the unit circle ⋮ Biorthogonal rational Krylov subspace methods

Cites Work

• Unnamed Item
• Convergence analysis of the extended Krylov subspace method for the Lyapunov equation
• The extended Krylov subspace method and orthogonal Laurent polynomials
• Orthogonal Laurent polynomials on the unit circle and snake-shaped matrix factorizations
• The QR algorithm for unitary Hessenberg matrices
• Unitary orthogonalization processes
• Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle
• Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
• CMV matrices: Five years after
• Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm
• A new investigation of the extended Krylov subspace method for matrix function evaluations
• Some Perspectives on the Eigenvalue Problem
• A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
• Approximation of Large-Scale Dynamical Systems
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• A Generalization of the Multishift QR Algorithm

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