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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A sweep-plane algorithm for generating random tuples in simple polytopes
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by Josef Leydold and Wolfgang Hörmann PDF
Math. Comp. 67 (1998), 1617-1635 Request permission

Abstract:

A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept through the given polytope until a random fraction (sampled from a proper univariate distribution) of the volume of the polytope is covered. Then the intersection of the plane with the polytope is a simple polytope with smaller dimension. In the second part we apply this method to construct a black-box algorithm for log-concave and $T$-concave multivariate distributions by means of transformed density rejection.
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Additional Information
  • Josef Leydold
  • Affiliation: University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria
  • Email: Josef.Leydold@wu-wien.ac.at
  • Wolfgang Hörmann
  • Affiliation: University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria; University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria
  • Address at time of publication: Boğaziçi University, Department of Industrial Engineering, 80815 Bebek-Istanbul, Turkey
  • Email: whoer@statrix2.wu-wien.ac.at
  • Received by editor(s): February 26, 1997
  • Received by editor(s) in revised form: August 18, 1997
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1617-1635
  • MSC (1991): Primary 65C10; Secondary 65C05, 68U20
  • DOI: https://doi.org/10.1090/S0025-5718-98-01004-7
  • MathSciNet review: 1604399