Title: Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions
Authors: Cools, Ronald * # ×
Kuo, Frances Y. * #
Nuyens, Dirk * #
Suryanarayana, Gowri * #
Issue Date: 2016
Publisher: Elsevier
Series Title: Journal of Complexity
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.
ISSN: 0885-064X
Publication status: accepted
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
* (joint) first author
× corresponding author
# (joint) last author

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