Convergence of the unitary QR algorithm with a unimodular Wilkinson shift

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:
2003

Citing 6
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Abstract

In applying the QR algorithm to compute the eigenvalues of a unitary Hessenberg matrix, a projected Wilkinson shift of unit modulus is proposed and proved to give global convergence with (at least) a quadratic asymptotic rate for the QR iteration. Experimental testing demonstrates that the unimodular shift produces more efficient numerical convergence.