On obtaining higher order convergence for smooth periodic functions

Authors:
Bart Vandewoestyne;Ronald Cools
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven,Celestijnenlaan 200A, B-3001 Heverlee, Belgium;Department of Computer Science, Katholieke Universiteit Leuven,Celestijnenlaan 200A, B-3001 Heverlee, Belgium
Venue:
Journal of Complexity
Year:
2008

Citing 2
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Weighted compound integration rules with higher order convergence for all N

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Abstract

We present two algorithms for multivariate numerical integration of smooth periodic functions. The cubature rules on which these algorithms are based use fractional parts of multiples of irrationals in combination with certain weights. Previous work led to algorithms with quadratic and cubic error convergence. We generalize these algorithms so that one can use them to obtain general higher order error convergence. The algorithms are open in the sense that extra steps can easily be taken in order to improve the result. They are also linear in the number of steps and their memory cost is low.