The Approach of Moments for Polynomial Equations

Monique Laurent () and Philipp Rostalski ()
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Monique Laurent: Centrum voor Wiskunde en Informatica
Philipp Rostalski: Johann Wolfgang Goethe-Universität

Chapter Chapter 2 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 25-60 from Springer

Abstract: Abstract 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.

Keywords: Real Root; Complex Root; Moment Matrix; Polynomial Optimization; Numerical Linear Algebra (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0769-0_2

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