Multivariate L∞ approximation in the worst case setting over reproducing kernel Hilbert spaces

@article{Kuo2008MultivariateLA,
title={Multivariate L∞ approximation in the worst case setting over reproducing kernel Hilbert spaces},
author={Frances Y. Kuo and Grzegorz W. Wasilkowski and Henryk Wozniakowski},
journal={Journal of Approximation Theory},
year={2008},
volume={152},
pages={135-160}
}

We study the worst case setting for approximation of d variate functions from a general reproducing kernel Hilbert space with the error measured in the L∞ norm. We mainly consider algorithms that use n arbitrary continuous linear functionals. We look for algorithms with the minimal worst case errors and for their rates of convergence as n goes to infinity. Algorithms using n function values will be analyzed in a forthcoming paper. We show that the L∞ approximation problem in the worst case… CONTINUE READING

Ritter, andG.W. Wasilkowski, Average case complexity of weighted integration and approximation over R for isotropic weights, in: K.-T. Fang, F.J. Hickernell, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer, Berlin • 2002