Title  An algebraist's view on border bases 
Author(s)  Achim Kehrein, Martin Kreuzer, Lorenzo Robbiano 
Type  Book, Chapter in Book, Conference Proceeding 
Abstract  This chapter is devoted to laying the algebraic foundations
for border bases of ideals. Using an order ideal $\mathcal{O}$,
we describe a zerodimensional ideal {\em from the outside}.
The first and higher borders of $\mathcal{O}$ can be used
to measure the distance of a term from $\mathcal{O}$ and to define
$\mathcal{O}$border bases. We study their existence and uniqueness,
their relation to Gröbner bases, and their characterization in
terms of commuting matrices. Finally, we use border bases to
solve a problem coming from statistics. 
Keywords  border basis, order ideal, Gröbner basis, commuting matrices, design of experiments 
Length  33 
ISBN  3540243267 
File 

Language  English 
Series  Algorithms and Computation in Mathematics 
Volume  14 
Chapter  4 
Pages  160202 
Publisher  Springer Verlag 
Address  Heidelberg 
Year  2005 
Editor  A. Dickenstein and I. Emiris 
Edition  0 
Translation 
No 
Refereed 
Yes 
Book  Solving Polynomial Equations: Foundations, Algorithms, and Applications 
Conferencename  CIMPA School 2003 (Buenos Aires/Argentina) 