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- B R H U N T, A L Nay, +6 authors A V Z I M I N
- 2003

A B S T R A C T Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively… (More)

- Thomas Sauer
- WETICE
- 2003

- Thomas Sauer, Yuan Xuy
- 1994

Lagrange interpolation by polynomials in several variables is studied through a nite diierences approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of the nite diierences. We prove that the nite diierence admits an integral representation involving sim-plex spline functions. In… (More)

Multivariate polynomial interpolation is a basic and fundamental subject in Approximation Theory and Numerical Analysis, which has received and continues receiving not deep but constant attention. In this short survey we review its development in the rst 75 years of this century, including a pioneering paper by Kronecker in the 19th century. x1.… (More)

- THOMAS SAUER
- 1994

The paper is concerned with a construction for H–bases of polynomial ideals without relying on term orders. The main ingredient is a homogeneous reduction algorithm which orthogonalizes leading terms instead of completely canceling them. This allows for an extension of Buchberger's algorithm to construct these H–bases algorithmically. In addition, the close… (More)

- Thomas Sauer
- 1998

This paper investigates polynomial interpolation with respect to a nite set of appropriate linear functionals and the close relations to the Grr obner basis of the associated nite dimensional ideal.

- Thomas Sauer, Yuan Xuy
- 1995

We study the problem of Hermite interpolation by polynomials in several variables. A very general deenition of Hermite interpolation is adopted which consists of interpolation of consecutive chains of directional derivatives. We discuss the structure and some aspects of poisedness of the Hermite interpolation problem; using the notion of blockwise structure… (More)

This paper summarizes relations between the constructive theory of polynomial ideals and polynomial interpolation in several variables. The main ingredient is a generalization of the algorithm for division with remainder to \quotients" of polynomials and nite sets of polynomi-als. x1. Introduction When compared to the univariate case, polynomial… (More)

This paper describes the development of the generic collaboration support architecture CAKE incorporating case-based reasoning (CBR). CAKE provides unified access to knowledge available within an organization, and CBR technology is used throughout the system to distribute this knowledge to agents as required. Adaptive workflows and collaboration patterns… (More)

- Thomas Sauer
- 1994

In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these… (More)