Fast Approximation of the Discrete Gauss Transform in Higher Dimensions

Authors:
Michael Griebel;Daniel Wissel
Affiliations:
Institute for Numerical Simulation, University of Bonn, Bonn, Germany 53115;Institute for Numerical Simulation, University of Bonn, Bonn, Germany 53115
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares favorably to existing methods especially when it comes to higher dimensions and a broad range of bandwidths. Numerical results with different datasets in up to 62 dimensions demonstrate its performance.