Abstract
In this paper we set out to understand Filon-type quadrature of highly-oscillating integrals of the form ∫ 1 0 f(x)e iωg(x) dx, where g is a real-valued function and ω >> 1. Employing ad hoc analysis, as well as perturbation theory, we demonstrate that for most functions g of interest the moments behave asymptotically according to a specific model that allows for an optimal choice of quadrature nodes. Filen-type methods that employ such quadrature nodes exhibit significantly faster decay of the error for high frequencies ω. Perhaps counterintuitively, as long as optimal quadrature nodes are used, rapid oscillation leads to significantly more precise and more affordable quadrature.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
