Comparison of Two Search Criteria for Lattice-based Kernel Approximation

04/04/2023

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by   Frances Y. Kuo, et al.

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The kernel interpolant in a reproducing kernel Hilbert space is optimal in the worst-case sense among all approximations of a function using the same set of function values. In this paper, we compare two search criteria to construct lattice point sets for use in lattice-based kernel approximation. The first candidate, _n^*, is based on the power function that appears in machine learning literature. The second, _n^*, is a search criterion used for generating lattices for approximation using truncated Fourier series. We find that the empirical difference in error between the lattices constructed using _n^* and _n^* is marginal. The criterion _n^* is preferred as it is computationally more efficient and has a proven error bound.