Geodesic
On the randomized complexity of Banach space valued integration
Stefan Heinrich 1   ; Aicke Hinrichs 2
1 Department of Computer Science University of Kaiserslautern D-67653 Kaiserslautern, Germany
2 Institute of Analysis Johannes Kepler University Linz Altenberger Str. 69 A-4040 Linz, Austria
Studia Mathematica, Tome 223 (2014) no. 3, pp. 205-215 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the complexity of Banach space valued integration in the randomized setting. We are concerned with $r$ times continuously differentiable functions on the $d$-dimensional unit cube $Q$, with values in a Banach space $X$, and investigate the relation of the optimal convergence rate to the geometry of $X$. It turns out that the $n$th minimal errors are bounded by $cn^{-r/d-1+1/p}$ if and only if $X$ is of equal norm type $p$.
DOI : 10.4064/sm223-3-2
Keywords: study complexity banach space valued integration randomized setting concerned times continuously differentiable functions d dimensional unit cube values banach space investigate relation optimal convergence rate geometry turns out nth minimal errors bounded r d only equal norm type nbsp

Stefan Heinrich  1   ; Aicke Hinrichs  2

1 Department of Computer Science University of Kaiserslautern D-67653 Kaiserslautern, Germany
2 Institute of Analysis Johannes Kepler University Linz Altenberger Str. 69 A-4040 Linz, Austria 
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Stefan Heinrich; Aicke Hinrichs. On the randomized complexity of
 Banach space valued integration. Studia Mathematica, Tome 223 (2014) no. 3, pp. 205-215. doi: 10.4064/sm223-3-2

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