Geodesic
Pseudoinverse operators. Properties and applications
Sbornik. Mathematics, Tome 46 (1983) no. 1, pp. 17-50

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This article studies the formalism and the problem of stability of pseudoinversion for closed densely defined operators in Hilbert spaces. The finite-dimensional version is also analyzed, because it is nontrivial and has numerous applications. Bibliography: 11 titles. 
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     author = {Yu. P. Pyt'ev},
     title = {Pseudoinverse operators. {Properties} and applications},
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Yu. P. Pyt'ev. Pseudoinverse operators. Properties and applications. Sbornik. Mathematics, Tome 46 (1983) no. 1, pp. 17-50. http://geodesic.mathdoc.fr/item/SM_1983_46_1_a1/