@Article{JCM-23-233, author = {}, 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 = {

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 $\mathbb{Z}_+^d$.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8812.html} }