Asymptotic Behavior of Automatic Quadrature

Numerical Quadrature and Asymptotic Expansions

Automatic differentiation of quadrature

We analyse the application of automatic differentiation (AD) to the quadrature (numerical integration) of a function integrand to determine the sensitivities of the integral to variation in the limits of integration. We derive an expression for the truncation errors of such ADderived sensitivities and relate them to the truncation error of the original, and a closely related, function quadratur...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic expansion and quadrature of composite highly oscillatory integrals

We consider in this paper asymptotic and numerical aspects of highly oscillatory integrals of the form ∫ b a f(x)g(sin[ωθ(x)])dx, where ω 1. Such integrals occur in the simulation of electronic circuits, but they are also of independent mathematical interest. The integral is expanded in asymptotic series in inverse powers of ω. This expansion clarifies the behaviour for large ω and also provide...

Asymptotic behavior of ACMA

The algebraic constant modulus algorithm (ACMA) is a noniterative blind source separation algorithm. It computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem. In this paper we analyze its asymptotic properties and show that (unlike the iterative CMA) it converges to the Wiener solution in samples or SNR. We also sketch its conne...