Uniformly distributed sequences in the orthogonal group and on the Grassmannian manifold

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Abstract

We construct and implement a uniformly distributed sequence in the orthogonal group O(n). From this sequence we obtain a uniformly distributed sequence on the Grassmannian manifold G(n,k), which we use to approximate integral-geometric formulas. We show that our algorithm compares well with classical random constructions which motivates various directions for future research.

Original languageEnglish
Pages (from-to)13-22
Number of pages10
JournalMathematics and Computers in Simulation
Volume160
Early online date12 Dec 2018
DOIs
Publication statusPublished - 01 Jun 2019

Keywords

  • Compact topological group
  • Crofton formula
  • Grassmannian manifold
  • Orthogonal group
  • Uniform distribution

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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