On counterexamples in multivariate approximation
On cubature formulae of degree 4k + 1 attaining Möller's lower bound for integrals with circular symmetry.
On Cubature Formulae with a Minimal Number of Knots.
On Equally Weighted Quadratures.
On error bounds for Gauss-Legendre and Lobatto quadrature rules.
On Gauss Quadrature Formulas with Equal Weights.
On generalizations of Ostrowski inequality via Euler harmonic identities.
On numerical cubatures of singular surface integrals in boundary element methods.
On one method of numerical integration
The uniform convergence of a sequence of Lienhard approximation of a given continuous function is proved. Further, a method of numerical integration is derived which is based on the Lienhard interpolation method.
On Optimal Chebyshev-Type Quadratures.
On optimal quadrature formulae.
On p-Generator Fully Symmetric Quadrature Rules.
On quadrature rules, inequalities and error bounds.
On Quasi Degree Quadrature Rules.
On Simpson's inequality and applications.
On some quadrature rules with Laplace end corrections
We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σi=1∞ f(i + 1/2) where f ∈ C 6 with its sixth derivative of constant sign on [m, ∞) and ∫ m∞ f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections,...
On some shift invariant integral operators, univariate case
In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and...
On the Construction of Multi-Dimensional Embedded Cubature Formulae.
On the Convergence of a Quadrature Rule for Evaluating Certain Cauchy Principal Value Integrals: An Addendum.
On the Convergence of a Quadrature Rule for Evaluating Certain Cauchy Principal Value Integrals.