### CAS Seminar

# Alexandre Monnet

### (Jacobs University)

## "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.