The Generalized Fibonacci Grid as Low-Discrepancy Point Set for Optimal Deterministic Gaussian Sampling

Daniel Frisch, Uwe D. Hanebeck

Abstract: We propose a multivariate Gaussian sampling scheme. The samples exhibit an “optimal deterministic” configuration. This entails better quadrature or cubature results than with random or quasi-random samples. Our sampling is based on the generalized Fibonacci grid that makes there markable properties of the well-known two-dimensional Fibonacci grid applicable in higher dimensions. Two options for generating the multivariate generalized Fibonacci grid are presented, based on a rotated grid and a linear programming counter, respectively. Various options for covariance matching are explored to obtain an unscented transform.