Mathematics

Research data from J.B. Lasserre and colleagues update understanding of computational mathematics

  2008 NOV 17 - (VerticalNews.com) -- According to recent research from Toulouse, France, "For an ideal I subset of R[x] given by a set of generators, a new semidefinite characterization of its real radical I(V-R(I)) is presented, provided it is zero-dimensional (even if I is not)."

  "Moreover, we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety V-R(I) as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Grobner basis," wrote J.B. Lasserre and colleagues.

  The researchers concluded: "The algorithm is based on moment relaxations and, in contrast to other existing methods, it exploits the real algebraic nature of the problem right from the beginning and avoids the computation of complex components."

  Lasserre and colleagues published their study in Foundations of Computational Mathematics (Semidefinite characterization and computation of zero-dimensional real radical ideals. Foundations of Computational Mathematics, 2008;8(5):607-647).

  For additional information, contact J.B. Lasserre, LAAS CNRS, Toulouse, France.

  Publisher contact information for the journal Foundations of Computational Mathematics is: Springer, 233 Spring St., New York, NY 10013, USA.

  Keywords: Algebra, MathematicsComputational Mathematics.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.