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.
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Kuo, F.Y., Sloan, I.H., Woźniakowski, H. (2006). Lattice Rules for Multivariate Approximation in the Worst Case Setting. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_18
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DOI: https://doi.org/10.1007/3-540-31186-6_18
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