Complex Gaussian quadrature for oscillatory integral transforms (Q2856623)
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scientific article; zbMATH DE number 6220956
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complex Gaussian quadrature for oscillatory integral transforms |
scientific article; zbMATH DE number 6220956 |
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Complex Gaussian quadrature for oscillatory integral transforms (English)
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30 October 2013
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integral transforms
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orthogonal polynomials
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numerical integration
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oscillatory integrand
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unbounded intervals
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Gaussian quadrature rules
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Fourier integral
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The paper is devoted to a study of a numerical method for the approximate computation of highly oscillatory integrals over unbounded intervals. The method is based on the observation that it is sometimes possible to extend the idea of Gaussian quadrature rules to a setting involving a weight function that has changes of sign. In the special case of a Fourier integral, the rule obtained by this approach is well known, but the basic idea can be used in many other situations too, leading to plenty of interesting new methods.
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