Fast Multilevel Evaluation of 1-D Piecewise Smooth Radial Basis Function Expansions
نویسنده
چکیده
Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data in R. However, a direct evaluation of an n-center RBF expansion at m points requires O(nm) operations, which is prohibitively expensive as n,m increase. We present a new multilevel method for uniformly dense centers and points and d = 1, whose cost is only O(C(n + m)), where C depends on the desired evaluation accuracy. The method extends a previous work [21] to any piecewise smooth radial kernel, e.g., thin plate spline. The multilevel summation algorithm can be generalized to higher dimensions, and can be also applied beyond RBFs, e.g. to discrete integral transform evaluation and
منابع مشابه
Fast Multilevel Evaluation of Smooth Radial Basis Function Expansions
Abstract. Radial basis functions (RBFs) are a powerful tool for interpolating/approximating multidimensional scattered data. Notwithstanding, RBFs pose computational challenges, such as the efficient evaluation of an n-center RBF expansion at m points. A direct summation requires O(nm) operations. We present a new multilevel method whose cost is only O((n + m) ln(1/δ)), where δ is the desired a...
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