Kolmogorov and Linear Widths on Generalized Besov Classes in the Monte Carlo Setting
作者： Liqin Duan , Peixin Ye
DOI: 10.1007/978-3-642-24999-0_10
关键词:
摘要: In this paper, we studied the Kolmogorov and linear widths on generalized Besov classes \(B^\Omega_{p,\theta}\) in norm of L q Monte Carlo setting. Applying discretization technique some properties pseudo-s-scale, determined exact asymptotic orders for certain values parameters p, q, θ.
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sci-hub.se 参考文章(20)
Klaus-Dieter Bierstedt, Functional analysis : proceedings of the Essen conference Dekker. ,(1994)
A. S. Romanyuk, LINEAR WIDTHS OF THE BESOV CLASSES OF PERIODIC FUNCTIONS OF MANY VARIABLES. II Ukrainian Mathematical Journal. ,vol. 53, pp. 744- 761 ,(2001) , 10.1023/A:1013356019431
Erich Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis ,(1988)
Fang Gensun, Ye Peixin, Integration error for multivariate functions from anisotropic classes Journal of Complexity. ,vol. 19, pp. 610- 627 ,(2003) , 10.1016/S0885-064X(03)00012-8
Allan Pinkus, n-Widths in Approximation Theory ,(1985)
O. V. Fedunyk, Linear widths of the classes B p,θ Ω of periodic functions of many variables in the space L q Ukrainian Mathematical Journal. ,vol. 58, pp. 103- 117 ,(2006) , 10.1007/S11253-006-0053-1
Gensun Fang, Liqin Duan, The complexity of function approximation on Sobolev spaces with bounded mixed derivative by linear Monte Carlo methods Journal of Complexity. ,vol. 24, pp. 398- 409 ,(2008) , 10.1016/J.JCO.2007.11.001
Peter Mathé, Random approximation of Sobolev embeddings Journal of Complexity. ,vol. 7, pp. 261- 281 ,(1991) , 10.1016/0885-064X(91)90036-W
GenSun Fang, LiQin Duan, The information-based complexity of approximation problem by adaptive Monte Carlo methods Science in China Series A: Mathematics. ,vol. 51, pp. 1679- 1689 ,(2008) , 10.1007/S11425-008-0008-0
Liqin Duan, The best m-term approximations on generalized Besov classes MB q Ω θ with regard to orthogonal dictionaries Journal of Approximation Theory. ,vol. 162, pp. 1964- 1981 ,(2010) , 10.1016/J.JAT.2010.05.005