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Tractability of multivariate problems for standard and linear information in the worst case setting: Part I
2016
Journal of Approximation Theory
We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore, some of these linear functionals have the same norm as the linear operators. We then apply this error bound for linear (unweighted) tensor products. In this way we use negative tractability results known for linear functionals to conclude the same negative
doi:10.1016/j.jat.2016.02.017
fatcat:umtkcunfirddzbt5q2k655fxam