Fast evaluation of vector splines in three dimensions |
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Authors: | F Chen D Suter |
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Affiliation: | (1) Department of Electrical and Computer Systems Engineering, Monash University, Clayton Campus, 3168, Vic., Australia |
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Abstract: | Vector spline techniques have been developed as general-purpose methods for vector field reconstruction. However, such vector
splines involve high computational complexity, which precludes applications of this technique to many problems using large
data sets. In this paper, we develop a fast multipole method for the rapid evaluation of the vector spline in three dimensions.
The algorithm depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation
and a downward local Taylor series approximation. In comparison with the CPU time of direct calculation, which increases at
a quadratic rate with the number of points, the presented fast algorithm achieves a higher speed in evaluation at a linear
rate. The theoretical error bounds are derived to ensure that the fast method works well with a specific accuracy. Numerical
simulations are performed in order to demonstrate the speed and the accuracy of the proposed fast method. |
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Keywords: | 68Q25 65Y20 |
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