Highly oscillatory integrals of composite type arise in electronic engineering and their calculations are a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is constructed based on the classical theory orthogonal polynomials its nodes weights can be computed efficiently by using tools numerical linear algebra. An interestin...

Zero-sum Hebbian learning rules that reinforce well correlated inputs have been used by others to model the competitive self-organization of afferents from the lateral geniculate nucleus to produce orientation selectivity and ocular dominance columns. However, the application of these simple Hebbian rules to the development of direction selectivity (DS) is problematic because the best correlate...

Given a probability measure ν and a positive integer n. How to choose n knots and n weights such that the corresponding quadrature rule has the minimum worst-case error when applied to approximate the ν-integral of Lipschitz functions? This question has been considered by several authors. We study this question whithin the framework of Turing machine-based real computability and complexity theo...

Abstract We analyse the Gaussian wave packet transform. Based on Fourier inversion formula and a partition of unity, which is formed by collection basis functions, new representation square-integrable functions presented. Including rigorous error analysis, variants transform are then derived discretization integral via different quadrature rules. Gauss–Hermite quadrature, we introduce packets i...