Quantum mechanics

Norm (philosophy)

Gaussian quadrature

Applied mathematics

Omega

Operating system

Hilbert space

Gauss–Hermite quadrature

Computer science

Numerical integration

Gauss–Kronrod quadrature formula

Fourier series

Physics

Nyström method

Mathematics

Optics

Political science

Quadrature (astronomy)

Mathematical analysis

Gauss–Laguerre quadrature

Clenshaw–Curtis quadrature

Integral equation

Fourier transform

Space (punctuation)

Tanh-sinh quadrature

Gauss–Jacobi quadrature

AIP conference proceedings

In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_a^b e^{2\pi i\omega x}\varphi(x)d x$ with $\omega\in \mathbb{R}$ in the Hilbert space $W_2^{(2,1)}[a,b]$ of complex-valued functions. Furthermore, the explicit expressions for coefficients of the constructed optimal quadrature formulas are obtained. At the end of the paper some numerical results are presented.

Optimal quadrature formulas for computing of Fourier integrals in W2(m,m−1) space