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- W2014853427 abstract "Quadrature rules using higher order digital nets and sequences are known to exploit the smoothness of a function for numerical integration and to achieve an improved rate of convergence as compared to classical digital nets and sequences for smooth functions. A construction principle of higher order digital nets and sequences based on a digit interlacing function was introduced in [J. Dick, SIAM J. Numer. Anal., 45 (2007) pp.~2141--2176], which interlaces classical digital nets or sequences whose number of components is a multiple of the dimension. In this paper, we study the use of polynomial lattice point sets for interlaced components. We call quadrature rules using such point sets {em interlaced polynomial lattice rules}. We consider weighted Walsh spaces containing smooth functions and derive two upper bounds on the worst-case error for interlaced polynomial lattice rules, both of which can be employed as a quality criterion for the construction of interlaced polynomial lattice rules. We investigate the component-by-component construction and the Korobov construction as a means of explicit constructions of good interlaced polynomial lattice rules that achieve the optimal rate of the worst-case error. Through this approach we are able to obtain a good dependence of the worst-case error bounds on the dimension under certain conditions on the weights, while significantly reducing the construction cost as compared to higher order polynomial lattice rules." @default.
- W2014853427 created "2016-06-24" @default.
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- W2014853427 date "2015-09-01" @default.
- W2014853427 modified "2023-10-03" @default.
- W2014853427 title "Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces" @default.
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- W2014853427 doi "https://doi.org/10.1016/j.cam.2015.02.041" @default.
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