Name
Title | ||
|---|---|---|
Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure |
Abstract | ||
|---|---|---|
We present sharp bounds on the Kolmogorov probabilistic (N, δ)-width and p average N- width of multivariate Sobolev space with mixed derivative MW2r(Td), r = (r1 ..., rd), 1/2 r1 = ... = rv rv + 1 ≤ ... ≤ rd equipped with a Gaussian measure µ in Lq (Td), that is dN, δ (MW2r(Td)), µ, Lq (Td)) = (N-1 lnv-1 N)r1 ċ (ρ - 1)/2 (ln(v-1)/2 N) √ 1 + (1/N)ln(1/δ), dN(a) (MW2r(Td), µ, Lq (Td))p = (N-1 lnv-1 N)r1 ċ (ρ - 1)/2 (ln(v-1)/2 N), where 1 q 1 is depending only on the eigenvalues of the correlation operator of the measure µ (see (4)). |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1016/j.jco.2004.04.001 | J. Complexity |
Keywords | DocType | Volume |
sharp bound,rv rv,p average N,N-1 lnv-1 N,mixed derivative MW2r,multivariate Sobolev space,sobolev space with mixed derivative,average width,correlation operator,Kolmogorov probabilistic,Gaussian measure,gaussian measure,probabilistic width | Journal | 20 |
Issue | ISSN | Citations |
6 | Journal of Complexity | 4 |
PageRank | References | Authors |
0.67 | 15 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chen Guanggui | 1 | 6 | 1.50 |
| FANG GENSUN | 2 | 26 | 8.25 |