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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.
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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     title = {Numerical integration with highly oscillating weight functions},
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     year = {1970},
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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

[1] Hammer P. C., Wicke H. H.: Quadrature formulas involving derivatives of the integrand. Mathematics of Computation 69, 3-7 (1960). | DOI | MR | Zbl

[2] Mikloško J.: Numerical integration with weight functions cos kx, sin kx on the $[0,2 \pi/t]$, t = 1, 2, ... Aplikace matematiky, 3, 1969, 179-194. | MR

[3] Szegö C.: Orthogonal polynomials. American Mathematical Society, New York, 1959. | MR

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