The QR Algorithm Revisited

DOI10.1137/060659454zbMath1134.65028OpenAlexW2040116662MaRDI QIDQ5450282

David S. Watkins

Publication date: 19 March 2008

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/16656bd4486eca740e99327280ad2355a2d7f407

zbMATH Keywords

eigenvalueeigenvectorQR algorithmHessenberg form

Mathematics Subject Classification ID

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

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Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix ⋮ Efficient alternating least squares algorithms for low multilinear rank approximation of tensors ⋮ The dynamical functional particle method for multi-term linear matrix equations ⋮ Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle ⋮ The Joint Bidiagonalization of a Matrix Pair with Inaccurate Inner Iterations ⋮ Kernel polynomials from \(L\)-orthogonal polynomials ⋮ A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence ⋮ Numerical solution of linear eigenvalue problems ⋮ Using the Cauchy-Binet formula in the convergence proof of the tridiagonal QR algorithm with shifts ⋮ New exact algorithms for planar maximum covering location by ellipses problems ⋮ On orthogonal reduction to Hessenberg form with small bandwidth ⋮ An extended QR-solver for large profiled matrices

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