The Approach of Moments for Polynomial Equations

  • Monique LaurentEmail author
  • Philipp Rostalski
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 166)


In this chapter we present the moment based approach for computing all real solutions of a given system of polynomial equations. This approach builds upon a lifting method for constructing semidefinite relaxations of several nonconvex optimization problems, using sums of squares of polynomials and the dual theory of moments. A crucial ingredient is a semidefinite characterization of the real radical ideal, consisting of all polynomials with the same real zero set as the system of polynomials to be solved. Combining this characterization with ideas from commutative algebra, (numerical) linear algebra and semidefinite optimization yields a new class of real algebraic algorithms. This chapter sheds some light on the underlying theory and the link to polynomial optimization.


Real Root Complex Root Moment Matrix Polynomial Optimization Numerical Linear Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands
  2. 2.Tilburg UniversityTilburgThe Netherlands
  3. 3.Institut für MathematikJohann Wolfgang Goethe-UniversitätFrankfurt am MainGermany

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