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- W2963854577 abstract "We deal with lattices that are generated by the Vandermonde matrices associated to the roots of Chebyshev polynomials. If the dimension d of the lattice is a power of two, i.e. $$d=2^m, m in mathbb {N}$$ , the resulting lattice is an admissible lattice in the sense of Skriganov. We prove that these lattices are orthogonal and possess a lattice representation matrix with orthogonal columns and entries not larger than 2 (in modulus). In particular, we clarify the existence of orthogonal admissible lattices in higher dimensions. The orthogonality property allows for an efficient enumeration of these lattices in axis parallel boxes. Hence they serve for a practical implementation of the Frolov cubature formulas, which recently drew attention due to their optimal convergence rates in a broad range of Besov–Lizorkin–Triebel spaces. As an application, we efficiently enumerate the Frolov cubature nodes in the d-cube $$[-1/2,1/2]^d$$ up to dimension $$d=16$$ ." @default.
- W2963854577 created "2019-07-30" @default.
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- W2963854577 date "2017-06-26" @default.
- W2963854577 modified "2023-09-24" @default.
- W2963854577 title "On the orthogonality of the Chebyshev–Frolov lattice and applications" @default.
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- W2963854577 doi "https://doi.org/10.1007/s00605-017-1078-2" @default.
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