Distribution of points on spheres and approximation by zonotopes
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
It is proved that if we approximate the Euclidean ballB n in the Hausdorff distance up toɛ by a Minkowski sum ofN segments, then the smallest possibleN is equal (up to a possible logarithmic factor) toc(n)ε −2(n−1)/(n+2). A similar result is proved ifB n is replaced by a general zonoid inR n .
- J. Beck and W. Chen,Irregularities of Distribution, Cambridge Tracts in Mathematics # 89, 1987.
- U. Betke and P. McMullen,Estimating the sizes of convex bodies from projections, J. London Math. Soc.27 (1983), 525–538. CrossRef
- J. Bourgain, J. Lindenstrauss and V. Milman,Approximation of zonoids by zonotopes, Acta Math. (1988).
- T. Figiel, J. Lindenstrauss and V. Milman,The dimension of almost spherical sections of convex bodies, Acta Math.129 (1977), 53–94. CrossRef
- J. Linhart,Approximation of a ball by zonotopes using uniform distribution on the sphere, preprint.
- V. G. Mazja,Sobolev Spaces, Springer-Verlag, Berlin, 1985.
- Distribution of points on spheres and approximation by zonotopes
Israel Journal of Mathematics
Volume 64, Issue 1 , pp 25-31
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors