Geodesic
Strong rank revealing Cholesky factorization
Electronic transactions on numerical analysis, Tome 17 (2004), pp. 76-92
For any symmetric positive definite matrix we introduce a definition of strong rank revealing $\textcent $###$\sterling $###$\textcent $###

$ Cholesky (RRCh) factorization similar to the notion of strong rank revealing QR factorization developed in the joint work of Gu and Eisenstat. There are certain key properties attached to strong RRCh factorization, the importance of which is discussed by Higham in the context of backward stability in his work on Cholesky decomposition of semidefinite matrices. We prove the existence of a pivoting strategy which, if applied in addition to standard Cholesky decomposition, leads to a strong RRCh factorization, and present two algorithms which use pivoting strategies based on the idea of local maximum volumes to compute a strong RRCh decomposition.$

Classification : 65F30
Keywords: Cholesky decomposition, LU decomposition, QR decomposition, rank revealing, numerical rank, singular values, strong rank revealing QR factorization 
@article{ETNA_2004__17__a10,
     author = {Gu,  M. and Miranian,  L.},
     title = {Strong rank revealing {Cholesky} factorization},
     journal = {Electronic transactions on numerical analysis},
     pages = {76--92},
     year = {2004},
     volume = {17},
     zbl = {1069.65023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__17__a10/}
}
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AU  - Miranian,  L.
TI  - Strong rank revealing Cholesky factorization
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PY  - 2004
SP  - 76
EP  - 92
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__17__a10/
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%A Gu,  M.
%A Miranian,  L.
%T Strong rank revealing Cholesky factorization
%J Electronic transactions on numerical analysis
%D 2004
%P 76-92
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%U http://geodesic.mathdoc.fr/item/ETNA_2004__17__a10/
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%F ETNA_2004__17__a10
Gu,  M.; Miranian,  L. Strong rank revealing Cholesky factorization. Electronic transactions on numerical analysis, Tome 17 (2004), pp. 76-92. http://geodesic.mathdoc.fr/item/ETNA_2004__17__a10/