Transformed Rank-1 Lattices for high-dimensional approximation

Robert Nasdala, Daniel Potts

Published 2018-05-23Version 1

This paper describes an extension of Fourier approximation methods for multivariate functions defined on bounded domains to unbounded ones via a multivariate change of coordinate mapping. In this approach we adapt algorithms for the evaluation and reconstruction of multivariate trigonometric polynomials based on single and multiple reconstructing rank-1 lattices and make use of dimension incremental construction methods for sparse frequency sets. Various numerical tests confirm obtained theoretical results for the transformed methods.