A Piecewise Constant Algorithm for Weighted L1 Approximation over Bounded or Unbounded Regions in Rs

@article{Hickernell2005APC,
title={A Piecewise Constant Algorithm for Weighted L1 Approximation over Bounded or Unbounded Regions in Rs},
author={Fred J. Hickernell and Ian H. Sloan and Grzegorz W. Wasilkowski},
journal={SIAM J. Numerical Analysis},
year={2005},
volume={43},
pages={1003-1020}
}

Using Smolyak’s construction [S. A. Smolyak, Dokl. Akad. Nauk SSSR, 4 (1963), pp. 240–243], we derive a new algorithm for approximating multivariate functions over bounded or unbounded regions in Rs with the error measured in a weighted L1-norm. We provide upper bounds for the algorithm’s cost and error for a class of functions whose mixed first order partial derivatives are bounded in the L1-norm. In particular, we prove that the error and the cost (measured in terms of the number of function… CONTINUE READING