General formulas for the smoothed analysis of condition numbers

Peter Bürgisser; Felipe Cucker; Martin Lotz

doi:10.1016/j.crma.2006.05.014

General formulas for the smoothed analysis of condition numbers

Peter Bürgisser, Felipe Cucker, Martin Lotz

Research output: Contribution to journal › Article › peer-review

Abstract

We provide estimates on the volume of tubular neighborhoods around a subvariety Σ of real projective space, intersected with a disk of radius σ. The bounds are in terms of σ, the dimension of the ambient space, and the degree of equations defining Σ. We use these bounds to obtain smoothed analysis estimates for some conic condition numbers. To cite this article: P. Bürgisser et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). © 2006 Académie des sciences.

Original language	English
Pages (from-to)	145-150
Number of pages	5
Journal	Académie des Sciences. Comptes Rendus. Mathématique
Volume	343
Issue number	2
DOIs	https://doi.org/10.1016/j.crma.2006.05.014
Publication status	Published - 15 Jul 2006

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10.1016/j.crma.2006.05.014

http://dx.doi.org/10.1016/j.crma.2006.05.014

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title = "General formulas for the smoothed analysis of condition numbers",

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AU - Cucker, Felipe

AU - Lotz, Martin

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AB - We provide estimates on the volume of tubular neighborhoods around a subvariety Σ of real projective space, intersected with a disk of radius σ. The bounds are in terms of σ, the dimension of the ambient space, and the degree of equations defining Σ. We use these bounds to obtain smoothed analysis estimates for some conic condition numbers. To cite this article: P. Bürgisser et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). © 2006 Académie des sciences.

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DO - 10.1016/j.crma.2006.05.014

M3 - Article

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JO - Académie des Sciences. Comptes Rendus. Mathématique

JF - Académie des Sciences. Comptes Rendus. Mathématique

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ER -

General formulas for the smoothed analysis of condition numbers

Abstract

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