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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).

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