# Moment matrices, border bases and real radical computation

@article{Lasserre2013MomentMB, title={Moment matrices, border bases and real radical computation}, author={Jean B. Lasserre and Monique Laurent and Bernard Mourrain and Philipp Rostalski and Philippe Trebuchet}, journal={J. Symb. Comput.}, year={2013}, volume={51}, pages={63-85} }

## 29 Citations

Computing Real Radicals by Moment Optimization

- Mathematics, Computer ScienceISSAC
- 2021

A new algorithm for computing the real radical of an ideal I and, more generally, the S-radical of I is presented, which is based on convex moment optimization, and an effective, general stopping criterion is given on the degree to detect when the prime ideals lying over the annihilator are real.

On exact Reznick, Hilbert-Artin and Putinar's representations

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2021

On the Complexity of Computing Real Radicals of Polynomial Systems

- Mathematics, Computer ScienceISSAC
- 2018

A probabilistic algorithm of complexity sO(1) (nD)O(nr2r) to compute rational parametrizations for all irreducible components of the real algebraic set V ∩ Rn is given.

On Exact Polya, Hilbert-Artin and Putinar's Representations

- Mathematics, Computer ScienceArXiv
- 2018

This work provides a hybrid numeric-symbolic algorithm computing exact rational SOS decompositions for polynomials lying in the interior of the SOS cone, and proves that bit complexity estimates on output size and runtime are both polynomial in the degree of the inputPolynomial and simply exponential in the number of variables.

On Exact Polya and Putinar's Representations

- Mathematics, Computer ScienceISSAC
- 2018

This work provides a hybrid numeric-symbolic algorithm computing exact rational SOS decompositions for polynomials lying in the interior of the SOS cone and proves that bit complexity estimates on output size and runtime are both polynomial in the degree of the inputPolynomial and simply exponential in the number of variables.

Multivariate moment problems : applications of the reconstruction of linear forms on the polynomial ring

- Mathematics
- 2015

This thesis deals with the reconstruction of linear forms on the polynomial ring and its applications. We propose theoretical and algorithmic tools to solve multivariate moment problems: the…

Computing real radicals and S-radicals of polynomial systems

- Mathematics, Computer ScienceJ. Symb. Comput.
- 2021

Certified relaxation for polynomial optimization on semi-algebraic sets

- Mathematics, Computer Science
- 2013

In this paper, we describe a relaxation method to compute the minimal critical value of a real polynomial function on a semialgebraic set S and the ideal defining the points at which the minimal…

Exact relaxation for polynomial optimization on semi-algebraic sets

- Mathematics, Computer Science
- 2014

This paper shows that when the infimum of a real polynomial function f on a closed basic semialgebraic set and the points where this infimum is reached, a relaxation hierarchy constructed from the Karush-Kuhn-Tucker ideal is always exact and that the vanishing ideal of the KKT minimizer points is generated by the kernel of the associated moment matrix in that degree.

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