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.
On the error estimation in numerical methods
On the error of compound quadrature formulas for r-convex functions.
On the Evaluation of Certain Two-Dimensional Singular Integrals with Cauchy Kernels.
On the Existence of Optimal Integration Formulas for Analytic Functions.
On the midpoint quadrature formula for lipschitzian mappings and applications
On the midpoint quadrature formula for mappings with bounded variations and applications
On the monotonicity of sequences of quadrature formulae.
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the positivity of certain Cotes numbers.
On the positivity of ultraspherical type quadrature formulas with Jacobi abscissas.
On the randomized complexity of Banach space valued integration
We study the complexity of Banach space valued integration in the randomized setting. We are concerned with r times continuously differentiable functions on the d-dimensional unit cube Q, with values in a Banach space X, and investigate the relation of the optimal convergence rate to the geometry of X. It turns out that the nth minimal errors are bounded by if and only if X is of equal norm type p.
On the trapezoid quadrature formula and applications
On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals.