Die Interpolation durch Bernoulli'sche Funktionen
Difference operators from interpolating moving least squares and their deviation from optimality
We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp. 37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.
Difference operators from interpolating moving least squares and their deviation from optimality
We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.
Discrete L-Splines.
Eberlein integral and polynomial interpolation
Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes
We present a new method for generating a d-dimensional simplicial mesh that minimizes the Lp-norm, p > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method
Ein ableitungsfreies Restglied für die trigonometrische Interpolation periodischer analytischer Funktionen.
Ein verallgemeinerter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation.
Eine Bemerkung zur Konvergenz Hermitescher Interpolationsprozesse.
Eine Faktorisierung der bei der rationalen Interpolation auftretenden Matrizen.
Elementare Fehlerdarstellung für Abteilungen bei der Hermite-Interpolation.
Erratum. Barycentric Formulae for Cardinal (SINC-) Interpolants.
Error estimate for quadratic spline interpolating the first derivatives
Error estimation for finite element solutions on meshes that contain thin elements
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.
Estimates for spline projections
Estimation de l'erreur d'interpolation d'Hermite dans IR".
Estimations d'erreur pour des éléments finis droits presque dégénérés
Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation
We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates on squeezed...
Fast Leja points.
Fitting a -Smooth Function to Data II.