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.
Bibliographical noteFunding 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.
* 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