Nous exhibons des bornes de la fonction de distribution du conditionnement des matrices singulières. Pour ce but nous developpons une technique nouvelle pour analyser les volumes des tubes (par rapport a la distance de Fubini–Study) autour des sous-variétés algèbriques d'un espace projectif complex. Plus spécifiquement, nous demontrons des bornes supérieueres de volumes des intersections des tubes extrinsèques (autour des sous-variétés algébriques avec une autre variété algèbrique donnée).
We exhibit upper bounds for the probability distribution of the generalized condition number of singular complex matrices. To this end, we develop a new technique to study volumes of tubes about projective varieties in the complex projective space. As a main outcome, we show an upper bound estimate for the volume of the intersection of a tube with an equi-dimensional projective algebraic variety.
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Carlos Beltrán 1 ; Luis Miguel Pardo 1
@article{CRMATH_2005__340_12_915_0, author = {Carlos Beltr\'an and Luis Miguel Pardo}, title = {Upper bounds on the distribution of the condition number of singular matrices}, journal = {Comptes Rendus. Math\'ematique}, pages = {915--919}, publisher = {Elsevier}, volume = {340}, number = {12}, year = {2005}, doi = {10.1016/j.crma.2005.05.012}, language = {en}, }
TY - JOUR AU - Carlos Beltrán AU - Luis Miguel Pardo TI - Upper bounds on the distribution of the condition number of singular matrices JO - Comptes Rendus. Mathématique PY - 2005 SP - 915 EP - 919 VL - 340 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2005.05.012 LA - en ID - CRMATH_2005__340_12_915_0 ER -
Carlos Beltrán; Luis Miguel Pardo. Upper bounds on the distribution of the condition number of singular matrices. Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 915-919. doi : 10.1016/j.crma.2005.05.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.05.012/
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⁎ Research was partially supported by MTM2004-01167.
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