Sampling convex bodies: a random matrix approach
نویسندگان
چکیده
منابع مشابه
A Block-Wise random sampling approach: Compressed sensing problem
The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...
متن کاملRandom Points, Convex Bodies, Lattices
Assume K is a convex body in R, and X is a (large) finite subset of K. How many convex polytopes are there whose vertices come from X? What is the typical shape of such a polytope? How well the largest such polytope (which is actually convX) approximates K? We are interested in these questions mainly in two cases. The first is when X is a random sample of n uniform, independent points from K an...
متن کاملRandom Aspects of High-dimensional Convex Bodies
In this paper we study geometry of compact, not necessarily centrally symmetric, convex bodies in R. Over the years, local theory of Banach spaces developed many sophisticated methods to study centrally symmetric convex bodies; and already some time ago it became clear that many results, if valid for arbitrary convex bodies, may be of interest in other areas of mathematics. In recent years many...
متن کاملRandom Polytopes in Smooth Convex Bodies
Let K<= R be a convex body and choose points xl,x2 xn randomly, independently, and uniformly from K. Then Kn = conv {x, , . . . , *„} is a random polytope that approximates K (as n -») with high probability. Answering a question of Rolf Schneider we determine, up to first order precision, the expectation of vol K -vol Kn when K is a smooth convex body. Moreover, this result is extended to qu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-06-08615-1