Condition pp 439-465 | Cite as

Probabilistic Analysis of Conic Condition Numbers: II. The Real Case

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


Our final goal can be succinctly stated: we want to extend the main result of the preceding chapter to problems with real data. Again this boils down to providing bounds on the volume of tubes. However, the technical development is quite different. One of the key constituents of the proof of the main result of Chap.  20 is false over the reals. For this reason, a more sophisticated line of argument involving integrals of curvature and the kinematic formula is required.

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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