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Numerical computation of the fourier transform using Laguerre functions and the Fast Fourier Transform
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In this paper, the authors proposed a numerical technique for the computation of Fourier transforms using a bilateral expansion of the unknown transformed function with respect to Laguarre functions using trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform.Abstract:
In this paper we propose a numerical technique for the computation of Fourier transforms. It uses a bilateral expansion of the unknown transformed function with respect to Laguarre functions. The expansion coefficients are obtained via trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform. The convergence of the algorithm is analyzed and numerical results are presented which confirm that it works well.read more
Citations
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The Exponentially Convergent Trapezoidal Rule
TL;DR: It is shown that far from being a curiosity, the trapezoidal rule is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special functions, complex analysis, rational approximation, integral equations, and the computation of functions and eigenvalues of matrices and operators.
Journal ArticleDOI
On the Laguerre Method for Numerically Inverting Laplace Transforms
TL;DR: A new variant of the Laguerre method is presented based on using a previously developed version of the Fourier-series method to calculate the coefficients of theLaguerrre generating function, developing systematic methods for scaling, and using Wynn's (epsilon)-algorithm to accelerate convergence of the Higgs boson series when the LAGs do not converge to zero geometrically fast.
Journal ArticleDOI
Computing the Hilbert transform on the real line
TL;DR: In this article, a collocation method based on an expansion in rational eigenfunctions of the Hilbert transform operator is proposed, which is implemented through the Fast Fourier Transform.
Journal ArticleDOI
Reproducing kernel method of solving singular integral equation with cosecant kernel
Hong Du,JiHong Shen +1 more
TL;DR: A reproducing kernel method of solving singular integral equations (SIE) with cosecant kernel with advantages that the representation of exact solution is obtained in a reproducingkernel Hilbert space and accuracy in numerical computation is higher.
Journal ArticleDOI
Reproducing kernel method for solving Fredholm integro-differential equations with weakly singularity
TL;DR: This work has developed a reproducing kernel method for solving Fredholm integro-differential equations with weakly singular kernels in reproducingkernel Hilbert space that is efficient and scalable.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Journal ArticleDOI
Methods of Numerical Integration.
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III.—On a Quadrature Formula for Trigonometric Integrals.
TL;DR: In this article, the authors present a quadrature algorithm for the integral form where ψ(x) is a function with a limited number of turning points in the range of integration and k is a constant which may take up large values.