The Mathematical Institute, University of Oxford, Eprints Archive

Fast sparse kernel summation on Cartesian grids

Zhu, Shengxin and Wathen, A. J. (2014) Fast sparse kernel summation on Cartesian grids. Technical Report. SIAM, SISC. (Submitted)

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Abstract

This paper proposes a fast algorithm for sparse kernel summation on an arbitrary fine Cartesian grid in high dimensional space of N points. The algorithm takes advantage of the sparsity of the underlying kernel function and the feature of Cartesian grid. It is a scalable algorithm with a complexity of O(N). The success of the algorithm relies on a special data structure for a Cartesian grid, which reduces the storage for the N points from O(dN) to O(1), a constant, and thus transforms costly memory intensive operations to cheap computationally intensive operations. Numerical examples for 3D surface reconstruction are presented to illustrated the efficiency of the algorithm.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1820
Deposited By: Helen Taylor
Deposited On:14 Mar 2014 08:43
Last Modified:29 May 2015 19:30

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