Browsing by Subject "worst case setting"

Now showing 1 - 4 of 4

Access status: Restricted ,
Optymalna aproksymacja całki Itô funkcji deterministycznych regularnych oraz osobliwych
(Data obrony: 2014-06-27) Dębowski, Jacek
Wydział Matematyki Stosowanej
Access status: Restricted ,
Optymalna aproksymacja skalarnych nieautonomicznych problemów początkowych z osobliwościami
(Data obrony: 2015-06-19) Górz, Marcin
Wydział Matematyki Stosowanej
Access status: Open Access ,
Polynomials on the space of ω-ultradifferentiable functions
(2007) Grasela, Katarzyna
The space of polynomials on the space $D_{\omega}$ of $\omega$-ultradifferentiable functions is represented as the direct sum of completions of symmetric tensor powers of $D^{\prime}_{\omega}$.
Access status: Open Access ,
The use of integral information in the solution of a two-point boundary value problem
(2007) Drwięga, Tomasz
We study the worst-case ε-complexity of a two-point boundary value problem $u^{\prime\prime}(x)=f(x)u(x)$, $x \in [0,T]$, $u(0)=c$, $u^{\prime}(T)=0$, where $c,T \in \mathbb{R}$ ($c \neq 0$, $T \gt 0$) and $f$ is a nonnegative function with $r$ ($r\geq 0$) continuous bounded derivatives. We prove an upper bound on the complexity for linear information showing that a speed-up by two orders of magnitude can be obtained compared to standard information. We define an algorithm based on integral information and analyze its error, which provides an upper bound on the $\varepsilon$-complexity.