On the randomized complexity of Banach space valued integration

Stefan Heinrich, and Aicke Hinrichs. "On the randomized complexity of Banach space valued integration." Studia Mathematica 223.3 (2014): 205-215. <http://eudml.org/doc/286220>.

@article{StefanHeinrich2014,
abstract = {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 nth minimal errors are bounded by $cn^\{-r/d - 1 + 1/p\}$ if and only if X is of equal norm type p.},
author = {Stefan Heinrich, Aicke Hinrichs},
journal = {Studia Mathematica},
keywords = {complexity of integration; Banach space-valued integration; minimal error of integration; randomized algorithms; multilevel Monte Carlo algorithm; Banach space of equal norm type; optimal convergence},
language = {eng},
number = {3},
pages = {205-215},
title = {On the randomized complexity of Banach space valued integration},
url = {http://eudml.org/doc/286220},
volume = {223},
year = {2014},
}

TY - JOUR
AU - Stefan Heinrich
AU - Aicke Hinrichs
TI - On the randomized complexity of Banach space valued integration
JO - Studia Mathematica
PY - 2014
VL - 223
IS - 3
SP - 205
EP - 215
AB - 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 nth minimal errors are bounded by $cn^{-r/d - 1 + 1/p}$ if and only if X is of equal norm type p.
LA - eng
KW - complexity of integration; Banach space-valued integration; minimal error of integration; randomized algorithms; multilevel Monte Carlo algorithm; Banach space of equal norm type; optimal convergence
UR - http://eudml.org/doc/286220
ER -