E-viri
Odprti dostop
-
Batenkov, D; Friedland, O; Yomdin, Y
arXiv (Cornell University), 08/2013Paper, Journal Article
Let \(Q\) be a relatively compact subset in a Hilbert space \(V\). For a given \(\e>0\) let \(N(\e,Q)\) be the minimal number of linear measurements, sufficient to reconstruct any \(x \in Q\) with the accuracy \(\e\). We call \(N(\e,Q)\) a sampling \(\e\)-entropy of \(Q\). Using Dimensionality Reduction, as provided by the Johnson-Lindenstrauss lemma, we show that, in an appropriate probabilistic setting, \(N(\e,Q)\) is bounded from above by the Kolmogorov's \(\e\)-entropy \(H(\e,Q)\), defined as \(H(\e,Q)=\log M(\e,Q)\), with \(M(\e,Q)\) being the minimal number of \(\e\)-balls covering \(Q\). As the main application, we show that piecewise smooth (piecewise analytic) functions in one and several variables can be sampled with essentially the same accuracy rate as their regular counterparts. For univariate piecewise \(C^k\)-smooth functions this result, which settles the so-called Eckhoff conjecture, was recently established in \cite{Bat} via a deterministic "algebraic reconstruction" algorithm.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Vnos na polico
Trajna povezava
- URL:
Faktor vpliva
Dostop do baze podatkov JCR je dovoljen samo uporabnikom iz Slovenije. Vaš trenutni IP-naslov ni na seznamu dovoljenih za dostop, zato je potrebna avtentikacija z ustreznim računom AAI.
Leto | Faktor vpliva | Izdaja | Kategorija | Razvrstitev | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Baze podatkov, v katerih je revija indeksirana
Ime baze podatkov | Področje | Leto |
---|
Povezave do osebnih bibliografij avtorjev | Povezave do podatkov o raziskovalcih v sistemu SICRIS |
---|
Vir: Osebne bibliografije
in: SICRIS
To gradivo vam je dostopno v celotnem besedilu. Če kljub temu želite naročiti gradivo, kliknite gumb Nadaljuj.