Convergence of the shifted QR algorithm for unitary Hessenberg matrices

Authors:
Tai-Lin Wang;William B. Gragg
Affiliations:
Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan, Republic of China;Department of Mathematics, Naval Postgraduate School, Monterey, California
Venue:
Mathematics of Computation
Year:
2002

Citing 5
Cited 6

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Abstract

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.