Geodesic
Numerical integration with highly oscillating weight functions
Applications of Mathematics, Tome 15 (1970) no. 2, pp. 133-145.

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The paper describes a new numerical method for the computation of integrals with the weight function exp$(ikx)$, $k$ integer, which can be used for improper and multiple integrals. The compound rules of this method use parameters, of weighted quadratures of Gauss type which are tabulated for various $k$. The using of the method especially for high $k$ is demonstrated by numerical experiments.
DOI : 10.21136/AM.1970.103277
Classification : 65-55
Keywords: numerical analysis 
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     author = {Miklo\v{s}ko, Jozef},
     title = {Numerical integration with highly oscillating weight functions},
     journal = {Applications of Mathematics},
     pages = {133--145},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1970},
     doi = {10.21136/AM.1970.103277},
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     zbl = {0191.16304},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1970.103277/}
}
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Mikloško, Jozef. Numerical integration with highly oscillating weight functions. Applications of Mathematics, Tome 15 (1970) no. 2, pp. 133-145. doi : 10.21136/AM.1970.103277. http://geodesic.mathdoc.fr/articles/10.21136/AM.1970.103277/

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