Comparison of Two Search Criteria for Lattice-based Kernel Approximation

2023/04/04 by Frances Y. Kuo, Kuo, Frances Y., Weiwen Mo +7 · 1 citation
Computer Science · Engineering · #65D15 #65T40 #Advanced Data Compression Techniques #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2304.01685

openalex publication_date 2023/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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, \calP_n^*, is based on the power function that appears in machine learning literature. The second, \calS_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 \calP_n^* and \calS_n^* is marginal. The criterion \calS_n^* is preferred as it is computationally more efficient and has a proven error bound.

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