In this paper, the average σ-K width of Sobolev-Wiener classes S<sub>pq</sub><sup>r</sup> W with mixed smooth- ness in L<sub>q</sub>（R<sup>d</sup>） is studied for 1【...In this paper, the average σ-K width of Sobolev-Wiener classes S<sub>pq</sub><sup>r</sup> W with mixed smooth- ness in L<sub>q</sub>（R<sup>d</sup>） is studied for 1【q≤p【∞, and the weak asymptotical behavior of these quantities is obtained.展开更多
Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asympt...Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.展开更多
基金Supported by Beijing Natural Science Foundation (Project No. 1982005)
文摘In this paper, the average σ-K width of Sobolev-Wiener classes S<sub>pq</sub><sup>r</sup> W with mixed smooth- ness in L<sub>q</sub>（R<sup>d</sup>） is studied for 1【q≤p【∞, and the weak asymptotical behavior of these quantities is obtained.
基金supported by the Natural Science Foundation of China (Grant No.10671019)Research Fund for the Doctoral Program of Higher Education (Grant No.20050027007)
文摘Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.
