# Alexandre Monnet

## "Numerical integration of functions of a rapidly rotating phase"

 Date: Wed, October 9, 2019 Time: 14:15 Place: Research I Seminar Room

Abstract: We present an algorithm for the efficient numerical evaluation of integrals of the form $I(\omega) = \int_0^1 F( x,\mathrm e^{\mathrm i \omega x}; \omega) \, \mathrm d x$ for sufficiently smooth but otherwise arbitrary $$F$$ and $$\omega \gg 1$$. The method is entirely "black-box", i.e., does not require the explicit computation of moment integrals or other pre-computations involving $$F$$. Its performance is uniform in the frequency $$\omega$$. We prove that the method converges exponentially with respect to its order when $$F$$ is analytic and give a numerical demonstration of its error characteristics.