Sharp error bounds for some quadrature formulae and applications.
Sharp error bounds for the trapezoidal rule and Simpson's rule.
Sharp Estimates in Terms of Moduli of Smoothness for Compound Cubature Rules.
Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation.
Solving a class of multivariate integration problems via Laplace techniques
We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...
Some double integral inequalities and applications.
Some generalized error inequalities and applications.
Some inequalities connected with an approximate integration.
Some methods of numerical integration over a semi-infinite interval
Some new four-point quadrature formulas.
Some positive Cotes numbers for the Chebyshev weight function.
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Spherical quadrature formulas with equally spaced nodes on latitudinal circles.
Spline quasi-interpolants and quadrature formulas.
Splines in Numerical Integration
AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...
Stochastic Properties of Quadrature Formulas.
Suboptimal Kronrod extension formulae for numerical quadrature.
Sur les formules de quadrature numérique à nombre minimal de noeuds d'intégration.
Sur une formule de quadrature pour des fonctions entières
Szegő quadrature and frequency analysis.