Given a finite sequence U_N={u_1,…,u_N} of points contained in the d-dimensional unit torus, we consider the L^2 discrepancy between the integral of a given function and the Riemann sums with respect to translations of U_N. We show that with positive probability, the L^2 discrepancy of other sequences close to U_N in a certain sense preserves the order of decay of the discrepancy of U_N. We also study the role of the regularity of the given function.
Brandolini, L., Chen, W., Gigante, G., & Travaglini, G. (2009). Discrepancy for randomized Riemann sums. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137, 3177-3185.
Citazione: | Brandolini, L., Chen, W., Gigante, G., & Travaglini, G. (2009). Discrepancy for randomized Riemann sums. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 137, 3177-3185. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Discrepancy for randomized Riemann sums |
Autori: | Brandolini, L; Chen, W; Gigante, G; Travaglini, G |
Autori: | |
Data di pubblicazione: | 2009 |
Lingua: | English |
Rivista: | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
Appare nelle tipologie: | 01 - Articolo su rivista |