Abstract
We discuss orthogonal Chebyshev-Frolov lattices, their generating matrices and their use in Frolov cubature formula. We give a detailed account on coordinate-permuted systems that lead to fast computation and enumeration of such lattices. In particular, we explain the recurrences identified in (K. Suzuki and T. Yoshiki, Hiroshima Math. J., 49(1):139–159, 2019) via a plain constructive approach exhibiting a new hierarchical basis of polynomials. Dual Chebyshev-Frolov lattices and their generating matrices are also studied. Lattices enumeration in axis-parallel boxes is discussed.
Acknowledgement
I would like to thank the editor and the anonymous reviewer for carefully reading and providing valuable comments and suggestions on the paper.
Citation
Moulay Abdellah Chkifa. "On generation and enumeration of orthogonal Chebyshev-Frolov lattices." Hiroshima Math. J. 52 (2) 235 - 253, July 2022. https://doi.org/10.32917/h2021046
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