正交Chebyshev-Frolov格的生成与枚举

Pub Date : 2022-07-01 DOI:10.32917/h2021046

Moulay Abdellah Chkifa

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引用次数: 0

摘要

综述：我们讨论了正交Chebyshev-Frolov格、它们的生成矩阵以及它们在Frolov体积公式中的应用。我们详细地介绍了坐标置换系统，它导致了这种格的快速计算和枚举。特别是，我们通过一种简单的构造方法来解释（K.Suzuki和T.Yoshiki，Hiroshima Math.J.，49（1）:139-1592019）中确定的递归，该方法展示了多项式的新层次基础。还研究了对偶Chebyshev-Frolov格及其生成矩阵。讨论了轴平行盒中的格枚举。

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On generation and enumeration of orthogonal Chebyshev-Frolov lattices

Summary: 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.

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