Exponential convergence and tractability of multivariate integration for Korobov spaces
نویسندگان
چکیده
منابع مشابه
Exponential convergence and tractability of multivariate integration for Korobov spaces
In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the functions of this space are infinitely times differentiable. Weights of the Korobov space monitor the influence of each variable and each group of variables. We show that there are numerical integration rules which achie...
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We study multivariate integration in the worst case setting for weighted Korobov spaces of smooth periodic functions of d variables. We wish to reduce the initial error by a factor ε for functions from the unit ball of the weighted Korobov space. Tractability means that the minimal number of function samples needed to solve the problem is polynomial in ε−1 and d. Strong tractability means that ...
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We study the approximation problem (or problem of optimal recovery in the L2norm) for weighted Korobov spaces with smoothness parameter α. The weights γj of the Korobov spaces moderate the behavior of periodic functions with respect to successive variables. The non-negative smoothness parameter α measures the decay of Fourier coefficients. For α = 0, the Korobov space is the L2 space, whereas f...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2011
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-2010-02433-0