Weighted Tensor Product Algorithms for Linear Multivariate Problems

@article{Wasilkowski1999WeightedTP,
  title={Weighted Tensor Product Algorithms for Linear Multivariate Problems},
  author={Grzegorz W. Wasilkowski and Henryk Wozniakowski},
  journal={J. Complex.},
  year={1999},
  volume={15},
  pages={402-447}
}
Abstract We study the e -approximation of linear multivariate problems defined over weighted tensor product Hilbert spaces of functions f of d variables. A class of weighted tensor product (WTP) algorithms is defined which depends on a number of parameters. Two classes of permissible information are studied. Λ all consists of all linear functionals while Λ std consists of evaluations of f or its derivatives. We show that these multivariate problems are sometimes tractable even with a worst-case… 
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