Convergence of the unitary $QR$ algorithm with a unimodular Wilkinson shift

DOI10.1090/S0025-5718-02-01444-8zbMath1014.65027MaRDI QIDQ4780377

Tai-Lin Wang, William B. Gragg

Publication date: 19 November 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

global convergenceeigenvaluesnumerical experimentsQR algorithmunitary Hessenberg matricesshift strategyunitary Hessenberg matrixWilkinson shift

Mathematics Subject Classification ID

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

Related Items

Sensitivity analysis for Szegő polynomials, Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle, The bisection eigenvalue method for unitary Hessenberg matrices via their quasiseparable structure, Compression of unitary rank-structured matrices to CMV-like shape with an application to polynomial rootfinding, Eigenvalue computation for unitary rank structured matrices, Rational \(QR\)-iteration without inversion, Unitary rank structured matrices, On tridiagonal matrices unitarily equivalent to normal matrices, Structured Eigenvalue Problems, A comparison between the complex symmetric based and classical computation of the singular value decomposition of normal matrices, A unitary Hessenberg \(QR\)-based algorithm via semiseparable matrices, A CS decomposition for orthogonal matrices with application to eigenvalue computation

Cites Work

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• The QR algorithm for real Hessenberg matrices
• Global convergence of tridiagonal QR algorithm with origin shifts
• Convergence of the shifted $QR$ algorithm for unitary Hessenberg matrices