Moment Matrices, Border Bases and Real Radical Computation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Symbolic Computation Year : 2013

Moment Matrices, Border Bases and Real Radical Computation


In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finite. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite programming. While the border basis algorithms of [17] are efficient and numerically stable for computing complex roots, algorithms based on moment matrices [12] allow the incorporation of additional polynomials, e.g., to re- strict the computation to real roots or to eliminate multiple solutions. The proposed algorithm can be used to compute a border basis of the input ideal and, as opposed to other approaches, it can also compute the quotient structure of the (real) radical ideal directly, i.e., without prior algebraic techniques such as Gr ̈obner bases. It thus combines the strength of existing algorithms and provides a unified treatment for the computation of border bases for the ideal, the radical ideal and the real radical ideal.
Fichier principal
Vignette du fichier
paper-hal.pdf (276.44 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00651759 , version 1 (14-12-2011)



Jean-Bernard Lasserre, Monique Laurent, Bernard Mourrain, Philipp Rostalski, Philippe Trébuchet. Moment Matrices, Border Bases and Real Radical Computation. Journal of Symbolic Computation, 2013, 51, pp.63-85. ⟨10.1016/j.jsc.2012.03.007⟩. ⟨hal-00651759⟩
513 View
286 Download



Gmail Facebook X LinkedIn More