Geodesic
Stability of the Schmidt orthogonalization operator
Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 811-834

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In this article we prove the existence of points of local instability of the Schmidt orthogonalization operator and classify them. We establish the quadratic stability of this operator in a neighborhood of a fixed point. 
@article{IM2_1970_4_4_a6,
     author = {A. M. Olevskii},
     title = {Stability of the {Schmidt} orthogonalization operator},
     journal = {Izvestiya. Mathematics },
     pages = {811--834},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a6/}
}
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A. M. Olevskii. Stability of the Schmidt orthogonalization operator. Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 811-834. http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a6/