Comptes Rendus
no. 12
Numerical Analysis
Upper bounds on the distribution of the condition number of singular matrices

Presented by: 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.

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.

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).

Received:
Accepted:
Published online:
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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Cited by Sources:

⁎ Research was partially supported by MTM2004-01167.

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