Convergence of the shifted QR algorithm for unitary Hessenberg matrices

This paper shows that for unitary Hessenberg matrices the QR algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with global convergence and cubic rates is also presented.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Tai-Lin Wang, William B. Gragg
• Keywords: Exceptional Initial-value Modification, Global Convergence, Hermitian Tridiagonal Matrices, MOC 2002