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Minimal and almost minimal rank 1 lattice rules, exact on trigonometric polynomials in two variables. (Russian. English summary) Zbl 1052.65013
A complete description is given for 2-dimensional lattice rules of rank 1 which are exact for algebraic or trigonometric polynomials of degree \(d\) (\(d\geq 1\) is arbitrary). The number of nodes for these cubature formulas is minimal or differs from minimal by one (for \(d\) even) or by two (for \(d\) odd).

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
65T40 Numerical methods for trigonometric approximation and interpolation
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