We study the error for quasi Monte Carlo quadrature rules on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and the worst case error for all functions in a given class of potentials. The main tools are the classical Kintchine-Marcinkiewicz-Zygmund inequality and more recent suitable de finitions of Sobolev classes on metric measure spaces.
Titolo: | Discrepancy and numerical integration in Sobolev spaces on metric measure spaces | |
Tutti gli autori: | Brandolini, Luca; Chen, William W. L.; Colzani, Leonardo; Gigante, Giacomo; Travaglini, Giancarlo | |
Data di pubblicazione: | 2013 | |
Abstract (eng): | We study the error for quasi Monte Carlo quadrature rules on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and the worst case error for all functions in a given class of potentials. The main tools are the classical Kintchine-Marcinkiewicz-Zygmund inequality and more recent suitable de finitions of Sobolev classes on metric measure spaces. | |
Nelle collezioni: | Working papers ENG. Mathematics and Statistics Series (2013- ) |
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