Geodesic
On the convergence of the $QR$ algorithm with multishifts
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 275-283

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A unified treatment of the cases of quadratic and cubic convergence of the $QR$ algorithm with multishifts is provided. The approach used is similar to that of Elsner and Watkins but does not use the notion of the distance between subspaces. Bibliography: 10 titles. 
@article{ZNSL_1995_229_a9,
     author = {E. E. Tyrtyshnikov},
     title = {On the convergence of the $QR$ algorithm with multishifts},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {275--283},
     publisher = {mathdoc},
     volume = {229},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_229_a9/}
}
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E. E. Tyrtyshnikov. On the convergence of the $QR$ algorithm with multishifts. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 275-283. http://geodesic.mathdoc.fr/item/ZNSL_1995_229_a9/