Details:
Title  From oil fields to Hilbert schemes.  Author(s)  Martin Kreuzer, Hennie Poulisse, Lorenzo Robbiano  Type  Book, Chapter in Book, Conference Proceeding  Abstract  New techniques for dealing with problems of numerical stability in computations involving multivariate polynomials allow a new approach to real world problems. Using a modelling problem for the optimization of oil production as a motivation, we present several recent developments involving border bases of polynomial ideals. After recalling the foundations of border basis theory in the exact case, we present a number of approximate techniques such as the eigenvalue method for polynomial system solving, the AVI algorithm for computing approximate border bases, and the SOI algorithm for computing stable order ideals. To get a deeper understanding for the algebra underlying this approximate world, we present recent advances concerning border basis and Gröbner basis schemes. They are open subschemes of Hilbert schemes and parametrize flat families of border bases and Gröbner bases. For the reader it will be a long, tortuous, sometimes dangerous, and hopefully fascinating journey from oil fields to Hilbert schemes.  Keywords  oil field polynomial system solving, eigenvalue method, BuchbergerMöller algorithm, border basis, approximate algorithm, border basis scheme  ISBN  9783211993132/pbk; 97832 
URL 
http://link.springer.com/chapter/10.1007%2F9783211993149_1 
Language  English  Pages  154  Publisher  Berlin: Springer  Year  2009  Edition  0  Translation 
No  Refereed 
No 
