Algebraic methods in approximation theory

Algebraic methods in approximation theory

This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis; their properties depend on combinatorics, topology, and geometry of a simplicial or polyhedral subdivision of a region in Rk, and are often quite subtle. We describe four algebraic technique...

Algebraic Methods in System Theory

Elegant algebraic theories for decomposing dynamical systems into elementary pieces have existed for some time in the areas of finite automata and linear systems. In contemporary physics, algebraic ideas, especially Lie algebras and Lie groups are used extensively to reveal and explain structure. This paper is an informal survey bringing together some of the important view points found in these...

Approximation Methods for Algebraic Curves and Surfaces

Methods of algebraic geometry in matrix theory

The purpose of these lectures to report on the recent solution of a 50 years old problem of describing the set of the eigenvalues of a sum of two hermitian matrices with prescribed eigenvalues 1 Statement of the problem For a field F denote by F the vector space of column vectors f = (f1, ..., fn) with entries in F. We will mostly assume that F is either the field of reals R or complexes C. We ...

Algebraic and analytic methods in graph theory