Gruber, Peter; matematični kolokvij april 2005

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Optimum Quantization

Peter Gruber

Technische Universität Wien, Avstrija

14. april 2005


Given a Jordan measurable set J on a Riemannian manifold, we consider the quality of the best possible distribution of n points on J as n tends to infinity. This result is then used to estimate

  1. the quality of encoders in data transmission systems,
  2. the error of numerical integration formulae,
  3. the best volume approximation of convex bodies by circumscribed convex polytopes,
  4. the minimum isoperimetric quotient of convex polytopes.
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