Eberlein integral and polynomial interpolation
Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
We propose two new algorithms to improve greedy sampling of high-dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the development of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a saturation assumption of the error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard greedy...
Eine Bemerkung zur Konvergenz Hermitescher Interpolationsprozesse.
Eine Faktorisierung der bei der rationalen Interpolation auftretenden Matrizen.
Equiconvergence of some sequences of rational functions.
Equiconvergence of some simultaneous Hermite-Padé interpolants
Erratum. Barycentric Formulae for Cardinal (SINC-) Interpolants.
Error bounds for two even degree tridiagonal splines.
Error estimate for quadratic spline interpolating the first derivatives
Error Estimates for Interpolatory Quadrature Formulae.
Error Estimates for Spline Interpolants on Equidistant Grids.
Estimates for En (Xn + 2m).
Estimates for the Lebesgue functions and the Nevai formula for the sinc-approximations of continuous functions on an interval.
Estimations de l'erreur d'approximation sur un domaine borné de Rn par Dm-splines d'interpolation et d'ajustement discrètes.
Estimations d'erreur pour des éléments finis droits presque dégénérés
Étude et convergence de fonctions «spline» complexes
Evaluation de l'erreur dans la méthode des éléments finis.
Extending n-convex functions
We are given data α₁,..., αₘ and a set of points E = x₁,...,xₘ. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions , i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.
Extension via interpolation
We suggest a modification of the Pawłucki and Pleśniak method to construct a continuous linear extension operator by means of interpolation polynomials. As an illustration we present explicitly the extension operator for the space of Whitney functions given on the Cantor ternary set.
Extensions and Selections in Subspaces of C(K).