Computing Discrepancies of Smolyak Quadrature Rules
نویسندگان
چکیده
In recent years, Smolyak quadrature rules (also called quadratures on hyperbolic cross points or sparse grids) have gained interest as a possible competitor to number theoretic quadratures for high dimensional problems. A standard way of comparing the quality of multivariate quadra-ture formulas consists in computing their L 2-discrepancy. Especially for larger dimensions, such computations are a highly complex task. In this paper we develop a fast recursive algorithm for computing the L 2-discrepancy (and related quality measures) of general Smolyak quadra-tures. We carry out numerical comparisons between the discrepancies of certain Smolyak rules, Hammersley and Monte Carlo sequences.
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ورودعنوان ژورنال:
- J. Complexity
دوره 12 شماره
صفحات -
تاریخ انتشار 1996