A Gauss quadrature rule for oscillatory integrands (Q5934216)
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scientific article; zbMATH DE number 1606152
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Gauss quadrature rule for oscillatory integrands |
scientific article; zbMATH DE number 1606152 |
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A Gauss quadrature rule for oscillatory integrands (English)
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19 June 2001
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oscillatory integrands
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Gauss quadrature rule
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0.9670448
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0.96172607
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0.94288385
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0.93974096
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0.92861104
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0.9272186
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0.9263937
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0.9196085
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The paper deals with the Gauss formula for the integral NEWLINE\[NEWLINE\int^1_{-1} y(x) dx\approx \sum^N_{k=1} w_k y(x_k).NEWLINE\]NEWLINE The authors present a procedure for calculating the weights \(w_k\) and the points \(x_k\), \(k= 1,\dots, N\), such that the formula is best tuned for oscillatory functions of the form: NEWLINE\[NEWLINEy(x)= f_1(x)\sin(\omega x)+ f_2(x)\cos(\omega x),NEWLINE\]NEWLINE where \(f_1(x)\) and \(f_2(x)\) are smooth.
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