Geodesic
Hermite interpolation and a method for evaluating Cauchy principal value integrals of oscillatory kind
Kragujevac Journal of Mathematics, Tome 29 (2006), p. 91

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An alternative method to the method proposed in [10] for the numerical evaluation of integrals of the form $\int_{-1}^1e^{i\phi t}f(t)dt$, where $f(t)$ has a simple pole in $(-1,1)$ and $\phi\in R$ may be large, has been developed. The method is based on a special case of Hermite interpolation polynomial and it is comparatively simpler and entails fewer function evaluations and thus faster, but the two methods are comparable in accuracy. The validity of the method is demonstrated in the provision of two numerical experiments and their results.
Classification : 65D32 41A55
Keywords: Hermite interpolation polynomial, oscillatory integrals, Cauchy principal value integral 
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     author = {G. E. Okecha},
     title = {Hermite interpolation and a method for evaluating {Cauchy} principal value integrals of oscillatory kind},
     journal = {Kragujevac Journal of Mathematics},
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     publisher = {mathdoc},
     volume = {29},
     year = {2006},
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     url = {http://geodesic.mathdoc.fr/item/KJM_2006_29_a8/}
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G. E. Okecha. Hermite interpolation and a method for evaluating Cauchy principal value integrals of oscillatory kind. Kragujevac Journal of Mathematics, Tome 29 (2006), p. 91 . http://geodesic.mathdoc.fr/item/KJM_2006_29_a8/