Integration and Approximation with Fibonacci lattice points

Abstract

We study the properties of a special rank-1 point set in 2 dimensions — Fibonacci lattice points. We present the analysis of these point sets for cubature and approximation of bivariate periodic functions with decaying spectral coefficients. We are interested in truncating the frequency space into index sets based on different degrees of exactness. The numerical results support that the Lebesgue constant of these point sets grows like the conjectured optimal rate ln 2 (N), where N is the number of sample points.