@Article{JCM-23-233,
author = {Xiao-Fei Hu and Pei-Xin Ye},
title = {Quantum Complexity of the Integration Problem for Anisotropic Classes},
journal = {Journal of Computational Mathematics},
year = {2005},
volume = {23},
number = {3},
pages = {233--246},
abstract = {<p style="text-align: justify;">We obtain the optimal order of high-dimensional integration complexity in the quantum computation model in anisotropic Sobolev classes $W_{\infty}^{\bf r}([0,1]^d)$ and Hölder Nikolskii classes $H_{\infty}^{\bf r}([0,1]^d)$. It is proved that for these classes of functions there is a speed-up of quantum algorithms over deterministic classical algorithms due to factor $n^{-1}$ and over randomized classical methods due to factor $n^{-1/2}$. Moreover, we give an estimation for optimal query complexity in the class $H_{\infty}^{\Lambda}(D)$ whose smoothness index is the boundary of some complete set in $\mathbb{Z}_+^d$. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8812.html}
}