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\iteman{io-port 01832380}
\itemau{Wang, Tai-Lin; Gragg, William B.}
\itemti{Convergence of the unitary $QR$ algorithm with a unimodular Wilkinson shift.}
\itemso{Math. Comput. 72, No.241, 375-385 (2003).}
\itemab
In a previous work, the authors showed that global convergence of the QR iteration is guaranteed with the Wilkinson shift in the unitary case, if only the starting value of the shift sequence is not zero, and an initial-value modification of the shift was proposed in the exceptional case. As a continuation, this paper deals with 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 a quadratic asymptotic rate for the QR iteration. Numerical experiments demonstrate the theoretical results.
\itemrv{Liu Xinguo (Qingdao)}
\itemcc{}
\itemut{QR algorithm; shift strategy; unitary Hessenberg matrices; numerical experiments; global convergence; Wilkinson shift; eigenvalues; unitary Hessenberg matrix}
\itemli{doi:10.1090/S0025-5718-02-01444-8 }
\end