Information-based complexity
Generalized tractability for multivariate problems Part I
Journal of Complexity
Tractability through increasing smoothness
Journal of Complexity
Journal of Complexity
Tractability of tensor product problems in the average case setting
Journal of Complexity
Average case tractability of non-homogeneous tensor product problems
Journal of Complexity
On tractability of approximation in special function spaces
Journal of Complexity
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We study d-variate approximation problems in the average case setting with respect to a zero-mean Gaussian measure. We consider algorithms that use finitely many evaluations of arbitrary linear functionals. For the absolute error criterion, we obtain the necessary and sufficient conditions in terms of the eigenvalues of its covariance operator and obtain an estimate of the exponent t^q^p^o^l^-^a^v^g of quasi-polynomial tractability which cannot be improved in general. For the linear tensor product problems, we find that the quasi-polynomial tractability is equivalent to the strong polynomial tractability. For the normalized error criterion, we solve a problem related to the Korobov kernels, which is left open in Lifshits et al. (2012).