Quadrature Coefficients for Sheppard's Formula (c)

Quadrature formula for computed tomography

We give a bivariate analog of the Micchelli-Rivlin quadrature for computing the integral of a function over the unit disk using its Radon projections. AMS subject classification: 65D32, 65D30, 41A55

Quadrature formulae for Fourier coefficients

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Michhelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a func...

Quadrature formula for sampled functions

Abstract—This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we upd...

Quadrature formulas for Fourier coefficients

Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space

Computation of integrals of strongly oscillating functions is one of the more important problems of numerical analysis, because such integrals are encountered in applications in many branches of mathematics as well as in other science such as quantum physics, flow mechanics and electromagnetism. Main examples of strongly oscillating integrands are encountered in different transformation, for ex...