Inequalities of Ostrowski type and applications in numerical integration.
Integral inequalities and computer algebra systems.
Integration in higher-order finite element method in 3D
Integration of Iterated Integrals by Multistep Methods.
Integro-differential equations with time-varying delay
Integro-differential equations with time-varying delay can provide us with realistic models of many real world phenomena. Delayed Lotka-Volterra predator-prey systems arise in ecology. We investigate the numerical solution of a system of two integro-differential equations with time-varying delay and the given initial function. We will present an approach based on -step methods using quadrature formulas.
Interpolation and integration based on averaged values
We discuss recent results on constructing approximating schemes based on averaged values of the approximated function f over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of f over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.
Interpolation operators on the space of holomorphic functions on the unit circle
The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval , , have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general...
Interpolatorische Kubaturformeln [Book]
Is Gauss Quadrature Optimal for Analytic Functions?
Konvergenzaussagen für Projektionsverfahren bei linearen Operatoren. - Convergence of Projection Methods for Linear Operators.
Kubaturformeln mit minimaler Knotenzahl. -Minimum-Point Cubature Formulas.
Low-discrepancy point sets for non-uniform measures
We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on there exists a point set whose star-discrepancy with respect to μ is of order . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...
Low-discrepancy point sets obtained by digital constructions over finite fields
Maximal order for quadratures using n evaluations.
Mean-Square Discrepancies of the Hammersley and Zaremba Sequences for Arbitrary Radix.
Mehrdimensionale Hermite-Interpolation und numerische Integration.
Metric theorems on the estimation of integrals by sums
Moment computation in shift invariant spaces.
Moment preserving spline approximation finite intervals and Chakalov-Popoviciu quadratures.
Monosplines and inequalities for the remainder term of quadrature formulas.