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Condition pp 233-254 | Cite as

Probabilistic Analyses of the GCC Condition Number

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

Abstract

In Chap.  6 we identified the GCC condition number as the crucial parameter in the perturbation theory of the polyhedral conic feasibility problem PCFP. Later on, we saw that this quantity occurs in cost estimates for an ellipsoid method finding feasible points in a nonempty cone and for interior-point methods deciding feasibility of polyhedral conic systems. Furthermore, the development in Chap.  10 showed that this condition number also plays a central role in cost estimates for deciding feasibility of primal–dual pairs in linear programming.

Continuing with one of the central themes in our exposition, we perform in this chapter probabilistic analyses of the GCC condition number, as was done in Chap.  2 for the condition number of linear equation solving. We obtain average and smoothed analysis estimates.

Keywords

Condition Number Convex Body Convex Cone Ellipsoid Method Angular Radius 
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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