Uniform approximation of vectors using adaptive randomized information

arXiv (Cornell University)

Abstract

We study approximation of the embedding $\ell_p^m \rightarrow \ell_{\infty}^m$, $1 \leq p \leq 2$, based on randomized adaptive algorithms that use arbitrary linear functionals as information on a problem instance. We show upper bounds for which the complexity $n$ exhibits only a $(\log\log m)$-dependence. Our results for $p=1$ lead to an example of a gap of order $n$ (up to logarithmic factors) for the error between best adaptive and non-adaptive Monte Carlo methods. This is the largest possible gap for linear problems.

Authors 1

1. Robert J. Kunsch Aachen at the Chair of Mathematics of Information Processing

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University , at the Chair of Mathematics of Information Processing , Pont- driesch 10 , 52062 Aachen ,