On an optimal quadrature formula for approximation of Fourier integrals in the space L-2((1))

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This paper deals with the construction of an optimal quadrature formula for approximation of Fourier integrals in the Sobolev space L-2((1)) [a, b] of non-periodic, complex valued functions which are square integrable with first order derivative. Here the quadrature sum consists of linear combination of the given function values in a uniform grid. The difference between the integral and the quadrature sum is estimated by the norm of the error functional. The optimal quadrature formula is obtained by minimizing the norm of the error functional with respect to coefficients. Analytic formulas for optimal coefficients can also be obtained using discrete analogue of the differential operator d(2)/dx(2). In addition, the convergence order of the optimal quadrature formula is studied. It is proved that the obtained formula is exact for all linear polynomials. Thus, it is shown that the convergence order of the optimal quadrature formula for functions of the space C-2[a, b] is O(h(2)). Moreover, several numerical resudlts are presented and the obtained optimal quadrature formula is applied to reconstruct the X-ray Computed Tomography image by approximating Fourier transforms.
Publisher
ELSEVIER
Issue Date
2020-07
Language
English
Article Type
Article
Citation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.372

ISSN
0377-0427
DOI
10.1016/j.cam.2020.112713
URI
http://hdl.handle.net/10203/273507
Appears in Collection
MA-Journal Papers(저널논문)
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