Uniqueness of Gaussian quadrature formula for computed tomography

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

Uniqueness of the Gaussian Quadrature for a Ball

We construct a formula for numerical integration of functions over the unit ball in R that uses n Radon projections of these functions and is exact for all algebraic polynomials in R of degree 2n&1. This is the highest algebraic degree of precision that could be achieved by an n term integration rule of this kind. We prove the uniqueness of this quadrature. In particular, we present a quadratur...

On the Universality of the Gaussian Quadrature Formula

Numerical integration over a disc. A new Gaussian quadrature formula

The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs and the beauty of these classical resul...

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...