Gaussian-type Quadrature Rules for Müntz Systems

Quadrature Rules for Fuzzy Integrals

Gaussian quadrature rules using function derivatives

Abstract: For finite positive Borel measures supported on the real line we consider a new type of quadrature rule with maximal algebraic degree of exactness, which involves function derivatives. We prove the existence of such quadrature rules and describe their basic properties. Also, we give an application of these quadrature rules to the solution of a Cauchy problem without solving it directl...

Müntz Systems and Orthogonal Müntz - Legendre Polynomials

The Müntz-Legendre polynomials arise by orthogonalizing the Müntz system {xxo, xx¡, ...} with respect to Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulae for the Müntz-Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros of Lague...

Gauss-type Quadrature Rules for Rational Functions

When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature ...

Error Bound of Certain Gaussian Quadrature Rules for Trigonometric Polynomials

In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function w(x) = 1+cosx, x ∈ (−π, π), for 2π-periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.