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- Tomas Sauer
- 2004

When passing from one to several variables, the nature and structure of polynomial interpolation changes completely: the solvability of the interpolation problem with respect to a given finite… (More)

Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains

- Rida T. Farouki, Tim N. T. Goodman, Tomas Sauer
- Computer Aided Geometric Design
- 2003

A scheme for constructing orthogonal systems of bivariate polynomials in the Bernstein–Bézier form triangular domains is formulated. The orthogonal basis functions have a hierarchical ordering by… (More)

- Jean-Louis Merrien, Tomas Sauer
- Adv. Comput. Math.
- 2012

Vector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function values and consecutive derivatives they differ by the “renormalization” of… (More)

- Mariano Gasca, Tomas Sauer
- Adv. Comput. Math.
- 2000

This is a survey of the main results on multivariate polynomial interpolation in the last twenty five years, a period of time when the subject experienced its most rapid development. The problem is… (More)

- Charles A. Micchelli, Tomas Sauer
- Adv. Comput. Math.
- 1997

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced… (More)

- Dietrich Braess, Tomas Sauer
- Journal of Approximation Theory
- 2004

When learning processes depend on samples but not on the order of the information in the sample, then the Bernoulli distribution is relevant and Bernstein polynomials enter into the analysis. We… (More)

- Alexander Klein, Tomas Sauer, Andreas Jedynak, Wolfgang Skrandies
- IEEE Transactions on Biomedical Engineering
- 2006

The use of coherence is a well-established standard approach for the analysis of biomedical signals. Being entirely based on frequency analysis, i.e., on spectral properties of the signal, it is not… (More)

- Gitta Kutyniok, Tomas Sauer
- SIAM J. Math. Analysis
- 2009

In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multireso-lution analysis with directional components. We will do so… (More)

- Tomas Sauer
- Adv. Comput. Math.
- 1995

The paper is concerned with the practical implementation of two methods to compute the solution of polynomial interpolation problems. In addition to a description of the implementation, practical… (More)

- Maria Charina, Costanza Conti, Tomas Sauer
- Numerical Algorithms
- 2004

In this paper we discuss methods for investigating the convergence of multivariate vector subdivision schemes and the regularity of the associated limit functions. Specifically, we consider… (More)