Average sampling numbers of multivariate periodic function spaces with a Gaussian measure

作者：Huang, Zexia; Wang, Heping^*

来源：Journal of Complexity, 2016, 36: 31-45.

DOI：10.1016/j.jco.2016.04.003

• Average sampling numbers
• Average approximation numbers
• Asymptotically optimal
• Gaussian measure

In this paper, we study average sampling numbers of the multivariate periodic function space L-2 with a Gaussian measure mu in the L-q metric for 1 <= q <= infinity, and obtain their asymptotical orders, where the Cameron-Martin space of the measure mu is an anisotropic periodic Sobolev space. Moreover, we show that in the average case setting, the Lagrange interpolating operators are asymptotically optimal linear algorithms in the L-q metric for all 1 <= q <= infinity. This is different from the situation in the worst case setting, where the Lagrange interpolating operators are not asymptotically optimal linear algorithms in the L-q metric for q = 1 or infinity.

• 出版日期2016-10
• 单位首都师范大学; 西华大学