Algorithms for Polyhedral Approximation of Multidimensional Ellipsoids

Mario A. Lopez; Shlomo Reisner

doi:10.1006/jagm.1999.1031

Algorithms for Polyhedral Approximation of Multidimensional Ellipsoids

Mario A. Lopez
, Shlomo Reisner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present efficient and simple algorithms for the approximation of a d-dimensional ellipsoid by polytopes of a prescribed size which are either contained in or contain the ellipsoid. The polytopes provided by our algorithms have a high degree of regularity, which enables us to construct their j-skeletons, j = 0, . . ., d - 1, efficiently. The rate of approximation, as measured by the symmetric distance and up to a constant, is best possible by any algorithm.

Original language	English
Pages (from-to)	140-165
Number of pages	26
Journal	Journal of Algorithms
Volume	33
Issue number	1
DOIs	https://doi.org/10.1006/jagm.1999.1031
State	Published - Oct 1999

Bibliographical note

Funding Information:
² Partially supported by the National Science Foundation Grant DMS-9626749 and by the Ann and Ullus Gudder Charitable Trust in the Mathematics and Computer Science Department of the University of Denver.

Funding Information:
* Partially supported by the National Science Foundation Grant DMS-9626749 and by the Colorado Advanced Software Institute Grant TT-9706.

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Computational Theory and Mathematics

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10.1006/jagm.1999.1031

Cite this

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author = "Lopez, \{Mario A.\} and Shlomo Reisner",

note = "Funding Information: ² Partially supported by the National Science Foundation Grant DMS-9626749 and by the Ann and Ullus Gudder Charitable Trust in the Mathematics and Computer Science Department of the University of Denver. Funding Information: * Partially supported by the National Science Foundation Grant DMS-9626749 and by the Colorado Advanced Software Institute Grant TT-9706.",

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AU - Reisner, Shlomo

N1 - Funding Information: ² Partially supported by the National Science Foundation Grant DMS-9626749 and by the Ann and Ullus Gudder Charitable Trust in the Mathematics and Computer Science Department of the University of Denver. Funding Information: * Partially supported by the National Science Foundation Grant DMS-9626749 and by the Colorado Advanced Software Institute Grant TT-9706.

PY - 1999/10

Y1 - 1999/10

N2 - We present efficient and simple algorithms for the approximation of a d-dimensional ellipsoid by polytopes of a prescribed size which are either contained in or contain the ellipsoid. The polytopes provided by our algorithms have a high degree of regularity, which enables us to construct their j-skeletons, j = 0, . . ., d - 1, efficiently. The rate of approximation, as measured by the symmetric distance and up to a constant, is best possible by any algorithm.

AB - We present efficient and simple algorithms for the approximation of a d-dimensional ellipsoid by polytopes of a prescribed size which are either contained in or contain the ellipsoid. The polytopes provided by our algorithms have a high degree of regularity, which enables us to construct their j-skeletons, j = 0, . . ., d - 1, efficiently. The rate of approximation, as measured by the symmetric distance and up to a constant, is best possible by any algorithm.

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DO - 10.1006/jagm.1999.1031

M3 - Article

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JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 1

ER -

Algorithms for Polyhedral Approximation of Multidimensional Ellipsoids

Abstract

Bibliographical note

ASJC Scopus subject areas

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