Comptes Rendus
no. 12
Numerical Analysis
Upper bounds on the distribution of the condition number of singular matrices
[Bornes supérieures pour la fonction de distribution du conditionnement des matrices singulières]

Présenté par : Philippe G. Ciarlet

Carlos Beltrán1 ; Luis Miguel Pardo1
1 Departamento de Matemáticas, Estadística y Computación, F. de Ciencias, Universidad de Cantabria, 39071 Santander, Spain
Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 915-919.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.05.012
Carlos Beltrán 1 ; Luis Miguel Pardo 1

1 Departamento de Matemáticas, Estadística y Computación, F. de Ciencias, Universidad de Cantabria, 39071 Santander, Spain 
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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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