Tractability of linear problems defined over Hilbert spaces |
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Authors: | Guiqiao Xu |
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Affiliation: | Department of Mathematics, Tianjin Normal University, Tianjin, 300387, PR China |
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Abstract: | We study d-variate approximation problems in the worst and average case settings. We consider algorithms that use finitely many evaluations of arbitrary linear functionals. In the worst case setting, we obtain necessary and sufficient conditions for quasi-polynomial tractability and uniform weak tractability. Furthermore, we give an estimate of the exponent of quasi-polynomial tractability which cannot be improved in general. In the average case setting, we obtain necessary and sufficient conditions for uniform weak tractability. As applications we discuss some examples. |
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Keywords: | Quasi-polynomial tractability Uniform weak tractability Linear problem Eigenvalue |
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