Name
Abstract | ||
|---|---|---|
We determine the asymptotic values on the linear probabilistic (N,δ)-widths and linear p-average N-widths of the space of multivariate functions with bounded mixed derivative MW2r(Td), r = (r1 ..... rd), 1/2 r1=...=rvrv+1≤ ... ≤rd equipped with a Gaussian measure µ in Lq (Td). That is, the following asymptotic equivalences hold: (1) If 1q≤2, then λN,δ(MW2r(Td),µ, Lq(Td)) = (N-1 lnv-1N)r1+(ρ-1)/2(ln(v-1)/2N) × √1+(1/N)ln(1/δ). (2) If 1 q N(a)(MW2r(Td),µ, Lq(Td)) = (N-1 lnv-1N)r1+(ρ-1/2)(ln(v-1)/2N). Here 0 1 depends only on the eigenvalues of the correlation operator of the measure µ (see (4)).If the dimension d ≥ 2, then the asymptotic exact order of probabilistic linear widths of MWr2(Td with the Gaussian measure µ in the Lq(Td) space for the cases q = 1, 2 q ≤ ∞ and the average linear widths λN(a) (MWr2(Td), µ, Lq(Td)) for the case q = 1 and q = ∞ are still open. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.jat.2004.10.012 | Journal of Approximation Theory |
Keywords | Field | DocType |
multivariate function space,asymptotic value,n-1 lnv-1n,gaussian measure,average linear width,linear probabilistic,multivariate function,case q,bounded mixed derivative mw,q n,probabilistic linear width,asymptotic exact order,correlation operator,cases q,linear p-average n-widths,function space,sobolev space | Function space,Mathematical optimization,Gaussian measure,Multivariate statistics,Mathematical analysis,Correlation,Operator (computer programming),Probabilistic logic,Eigenvalues and eigenvectors,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
132 | 1 | 0021-9045 |
Citations | PageRank | References |
2 | 0.49 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chen Guanggui | 1 | 6 | 1.50 |
| FANG GENSUN | 2 | 26 | 8.25 |