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arXiv · 1606.00648

Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions

Ronald Cools·Frances Y. Kuo·Dirk Nuyens·Gowri Suryanarayana
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Abstract

We develop algorithms for multivariate integration and approximation in the weighted half-period cosine space of smooth non-periodic functions. We use specially constructed tent-transformed rank-1 lattice points as cubature nodes for integration and as sampling points for approximation. For both integration and approximation, we study the connection between the worst-case errors of our algorithms in the cosine space and the worst-case errors of some related algorithms in the well-known weighted Korobov space of smooth periodic functions. By exploiting this connection, we are able to obtain constructive worst-case error bounds with good convergence rates for the cosine space.

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Ronald Cools, Frances Y. Kuo, Dirk Nuyens, Gowri Suryanarayana. 2016-06-02. Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions. https://doi.org/10.1016/j.jco.2016.05.004

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