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By Barutello V., Terracini S.

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L. Wang and W. B. Gragg. Convergence of the unitary QR algorithm with unitary Wilkinson shift. Mathematics of Computation, 72(241):375– 385, 2003. As already mentioned, unitary Hessenberg matrices have the upper triangular part in the matrix of semiseparable form. In the following paper by Gemignani the quasiseparable structure of the unitary Hessenberg matrix is exploited to develop a QR-algorithm. Moreover the presented algorithm is also valid for unitary Hessenberg plus rank 1 matrices. The presented method transforms the matrix into a hermitian semiseparable plus diagonal matrix via the M¨ obius transform, then a QR-method is applied for computing its eigenvalues.

T. Heath, editor, Hypercube multiprocessors 1987, pages 639–647, Philadelphia, 1987. SIAM. ☞ T. L. Wang and W. B. Gragg. Convergence of the shifted QR algorithm, for unitary Hessenberg matrices. Mathematics of Computation, 71(240):1473– 1496, 2002. ☞ T. L. Wang and W. B. Gragg. Convergence of the unitary QR algorithm with unitary Wilkinson shift. Mathematics of Computation, 72(241):375– 385, 2003. As already mentioned, unitary Hessenberg matrices have the upper triangular part in the matrix of semiseparable form.

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