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Quasi-polynomial tractability of linear problems in the average case setting
Authors:Guiqiao Xu
Institution:Department of Mathematics, Tianjin Normal University, Tianjin, 300387, PR China
Abstract:We study dd-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 tqpol-avgtqpol-avg 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).
Keywords:Quasi-polynomial tractability  Linear problem  Eigenvalue  Average case setting
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