Lattice Rules for Multivariate Approximation in the Worst Case Setting

Frances Y. Kuo (), Ian H. Sloan () and Henryk Woźniakowski ()
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Frances Y. Kuo: University of New South Wales, School of Mathematics
Ian H. Sloan: University of New South Wales, School of Mathematics
Henryk Woźniakowski: Columbia University, Department of Computer Science

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 289-330 from Springer

Abstract: Summary We develop algorithms for multivariate approximation in weighted Korobov spaces of smooth periodic functions of d variables. Our emphasis is on large d. The smoothness of functions is characterized by the parameter α>1 that controls the decay of Fourier coefficients in the L2 norm. The weight γj of the Korobov space moderates the behaviour of functions with respect to the jth variable. Small γj means that functions depend weakly on the jth variable.

Keywords: Approximation Problem; Generate Vector; Reproduce Kernel Hilbert Space; Integration Error; Lattice Rule (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_18

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DOI: 10.1007/3-540-31186-6_18

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