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1. Sampling numbers of periodic Sobolev spaces with a Gaussian measure in the average case setting

Author

Huang, Zexia and Wang, Heping

Subjects
*SOBOLEV spaces, *FUNCTION spaces, *GAUSSIAN measures, *LAGRANGE equations, *INTERPOLATION, *APPROXIMATION theory, *ASYMPTOTIC distribution, *ALGORITHMS
Abstract

Abstract: In this paper, we investigate -average sampling numbers of a periodic Sobolev space with a Gaussian measure in the metric for and , and obtain their asymptotic orders. Moreover, we show that in the average case setting, the operators , which are the Lagrange interpolating operators, are asymptotically optimal in the metric for all . It is interesting to note that in the worst case setting, are not asymptotically optimal algorithms in the metric for or . [Copyright &y& Elsevier]

Published
2013
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