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

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