Four-dimensional lattice rules generated by skew-circulant matrices

DOI10.1090/S0025-5718-03-01534-5zbMath1035.65026OpenAlexW2093425374MaRDI QIDQ4433132

Tor Sørevik, J. N. Lyness

Publication date: 29 October 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01534-5

zbMATH Keywords

quadrature and cubature formulastrigonometric approximationoptimal lattice rulesmultidimensional cubature\(K\)-optimal rulesoptimal trigonometric rulesskew-circulant matrices

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (19)

Trigonometric interpolation on lattice grids ⋮ The index of merit of \(k\)th-copy integration lattices ⋮ Extremal lattices and the construction of lattice rules ⋮ The inverse and the Moore-Penrose inverse of a \(k\)-circulant matrix with binomial coefficients ⋮ A new generalization of the Frank matrix and its some properties ⋮ The explicit identities for spectral norms of circulant-type matrices involving binomial coefficients and harmonic numbers ⋮ Isomorphic operators and functional equations for the skew-circulant algebra ⋮ On skew circulant type matrices involving any continuous Fibonacci numbers ⋮ Optimal backward perturbation analysis for the block skew circulant linear systems with skew circulant blocks ⋮ Explicit inverse matrices of Tribonacci skew circulant type matrices ⋮ Analysis of the structured perturbation for the BSCCB linear system ⋮ On \(k\)-circulant matrices involving the Pell-Lucas (and the modified Pell) numbers ⋮ On optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix ⋮ Good low degree rank-1 lattice rules of high dimension ⋮ The Hermite normal form for certain rank-1 circulant and skew-circulant lattice rules ⋮ Five-dimensional $K$-optimal lattice rules ⋮ Multidimensional pseudo-spectral methods on lattice grids ⋮ The determinants, inverses, norm, and spread of skew circulant type matrices involving any continuous Lucas numbers ⋮ On \(r\)-min and \(r\)-max matrices

Cites Work

• Three- and four-dimensional 𝐾-optimal lattice rules of moderate trigonometric degree
• An Introduction to Lattice Rules and their Generator Matrices
• Minimal cubature formulae of trigonometric degree
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