Geodesic
Convergence of Rump's method for computing the Moore-Penrose inverse
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 859-879.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the Moore-Penrose inverse.
DOI : 10.1007/s10587-016-0297-3
Classification : 15A24, 65F05
Keywords: Moore-Penrose inverse; condition number; ill-conditioned matrix 
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     title = {Convergence of {Rump's} method for computing the {Moore-Penrose} inverse},
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Chen, Yunkun; Shi, Xinghua; Wei, Yimin. Convergence of Rump's method for computing the Moore-Penrose inverse. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 859-879. doi : 10.1007/s10587-016-0297-3. http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0297-3/

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