Extensions of Fibonacci lattice rules

We study the trigonometric degree of pairs of embedded cubature rules for the approximation of two-dimensional integrals, where the basic cubature rule is a Fibonacci lattice rule. The embedded cubature rule is constructed by simply doubling the points which results in adding a shifted version of the basic Fibonacci rule. An explicit expression is derived for the trigonometric degree of this particular extension of the Fibonacci rule based on the index of the Fibonacci number. © Springer-Verlag Berlin Heidelberg 2009.status: publishe