AN EXPONENTIALLY WEIGHTED OPTIMAL QUADRATURE FORMULA IN THE SPACE (1,0) W 2 OF PERIODIC FUNCTIONS
Keywords:
The Hilbert space, the Fourier integrals, the Fourier coefficients, the error functional, periodic functions, the extremal function, optimal coefficients, optimal quadrature formula.Abstract
This work studies the problem of construction of the optimal quadrature
formula in the sense of Sard in the Hilbert space
W
(1,0)
2
0,1
of periodic, complex-valued
functions for numerical calculation of Fourier integrals. Here a quadrature sum consists of a
linear combination of the given function values on a uniform mesh. The optimal quadrature
formula is obtained by minimizing the norm of the error functional with respect to
coefficients.
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