Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm

DOI10.1137/100809167zbMath1218.65035OpenAlexW2018276414MaRDI QIDQ3008246

Raf Vandebril

Publication date: 15 June 2011

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

Full work available at URL: https://lirias.kuleuven.be/handle/123456789/280648

zbMATH Keywords

eigenvaluesnumerical experimentsGivens rotationsHessenberg matricesunitary similarity transformations\(CMV\)-matrix\(QR\)-type algorithmspatterns of rotations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

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An extended Hessenberg form for Hamiltonian matrices ⋮ An implicit filter for rational Krylov using core transformations ⋮ Data-dependent orthogonal polynomials on generalized circles: a unified approach applied to \(\delta \)-domain identification ⋮ An extended Hamiltonian QR algorithm ⋮ An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation ⋮ Deflating invariant subspaces for rank structured pencils ⋮ Efficient Reduction of Compressed Unitary Plus Low Rank Matrices to Hessenberg Form ⋮ Short recurrences for computing extended Krylov bases for Hermitian and unitary matrices ⋮ Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices ⋮ Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials ⋮ On the stability of computing polynomial roots via confederate linearizations ⋮ Biorthogonal rational Krylov subspace methods ⋮ A CMV-Based Eigensolver for Companion Matrices ⋮ A Core-Chasing Symplectic QR Algorithm ⋮ Orthogonal iterations on companion-like pencils

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