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Lattice Rules for Multivariate Approximation in the Worst Case Setting

In: Monte Carlo and Quasi-Monte Carlo Methods 2004

Author

Listed:
  • 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
    University of Warsaw, Institute of Applied Mathematics and Mechanics)

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.

Suggested Citation

  • Frances Y. Kuo & Ian H. Sloan & Henryk Woźniakowski, 2006. "Lattice Rules for Multivariate Approximation in the Worst Case Setting," Springer Books, in: Harald Niederreiter & Denis Talay (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 289-330, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-31186-7_18
    DOI: 10.1007/3-540-31186-6_18
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