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Condition pp 419-437 | Cite as

Probabilistic Analysis of Conic Condition Numbers: I. The Complex Case

  • Peter Bürgisser
  • Felipe Cucker
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 349)

Abstract

The smoothed analysis of condition numbers in the preceding chapters was done on a case-by-case basis. For each considered condition number we proved a result giving bounds on either expectation or probability tails or both. In this chapter and the next we proceed differently—the theme of both chapters is the same, but the focus of this is on problems over \(\mathbb {C}\), while the focus on the next is on problems over \(\mathbb {R}\). We consider a reasonably large class of condition numbers and obtain smoothed analysis estimates for elements in this class depending only on geometric invariants of the corresponding sets of ill-posed inputs.

Keywords

Condition Number Complex Projective Space Integral Geometry Smooth Submanifold Multiple Zero 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Peter Bürgisser
    • 1
  • Felipe Cucker
    • 2
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsCity University of Hong KongHong KongHong Kong SAR

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