Geodesic
LDU decompositions with $L$ and $U$ well conditioned
Electronic transactions on numerical analysis, Tome 18 (2004), pp. 198-208.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We present, for some classes of matrices, -decompositions whose unit triangular factors $\textcent $###$\sterling $########$ \textcent $and are simultaneously very well conditioned. Our examples include diagonally dominant matrices by rows and $$###$$ columns and their inverses, Stieljes matrices and -matrices diagonally dominant by rows or columns. We also § show a construction of an accurate computation of the -decomposition for any -matrix diagonally dominant $\textcent \ddot \sterling $########$$ {\S} by rows or columns, which in turn can be applied to obtain an accurate singular value decomposition.$$
Classification : 65F05, 65F35, 15A12
Keywords: conditioning, diagonal dominance, pivoting strategies, accuracy, singular value decomposition 
@article{ETNA_2004__18__a0,
     author = {Pe\~na, J.M.},
     title = {LDU decompositions with $L$ and $U$ well conditioned},
     journal = {Electronic transactions on numerical analysis},
     pages = {198--208},
     publisher = {mathdoc},
     volume = {18},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__18__a0/}
}
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Peña, J.M. LDU decompositions with $L$ and $U$ well conditioned. Electronic transactions on numerical analysis, Tome 18 (2004), pp. 198-208. http://geodesic.mathdoc.fr/item/ETNA_2004__18__a0/