Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.

# Computing the real variety of an ideal - A real algebraic and symbolicnumeric algorithm

 Author(s):M. Laurent, J.B. Lasserre, Ph. Rostalski Conference/Journal:Annual ACM Symposium on Applied Computing, Fortaleza, Ceará, Brazil Abstract:We provide a real algebraic symbolic-numeric algorithm for computing the real variety V_R(I) of an ideal I \in R[x], assuming V_R(I) is finite (while V_C(I) could be infinite). Our approach uses sets of linear functionals on R[x], vanishing on a given set of polynomials generating I and their prolongations up to a given degree, as well as on polynomials of the real radical ideal \sqrt[R]{I} obtained from the kernel of a suitably defined moment matrix assumed to be positive semidefinite and of maximum rank. We formulate a condition on the dimensions of projections of these sets of linear functionals, which serves as stopping criterion for our algorithm. This algorithm is based on standard numerical linear algebra routines and semidefinite optimization and combines techniques from previous work of the authors together with an existing algorithm for the complex variety. This results in a unified methodology for the real and complex cases. Year:2008 Type of Publication: (01)Article Supervisor: File Download: Request a copy of this publication. (Uses JavaScript) % Autogenerated BibTeX entry @InProceedings { LauLas:2008:IFA_3089, author={M. Laurent and J.B. Lasserre and Ph. Rostalski}, title={{Computing the real variety of an ideal - A real algebraic and symbolicnumeric algorithm}}, booktitle={Annual ACM Symposium on Applied Computing}, pages={}, year={2008}, address={Fortaleza, Cear{\'a}, Brazil}, month=mar, url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=3089} } Permanent link

 © 1999-2014 by ETH Zurich | Webmaster | Wednesday, May 23, 2018