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Fast, numerically stable computation of oscillatory integrals with stationary points

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 no...

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Publication date:
2009-05-05
URN:
uuid:8fd27e51-cc38-4c87-944c-01d4b79aa59f
Local pid:
oai:eprints.maths.ox.ac.uk:867

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