The Mathematical Institute, University of Oxford, Eprints Archive

Fast, numerically stable computation of oscillatory integrals with stationary points

Olver, Sheehan (2009) Fast, numerically stable computation of oscillatory integrals with stationary points. Technical Report. Unspecified. (Submitted)

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Abstract

We present a numerically stable way to compute oscillatory integrals of the form $\int{-1}^{1} f(x)e^{i\omega g(x)}dx$. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the first stable algorithm for oscillatory integrals with stationary points which does not lose accuracy as the frequency increases and does not require deformation into the complex plane.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:867
Deposited By:Lotti Ekert
Deposited On:17 Dec 2009 08:08
Last Modified:17 Dec 2009 08:08

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