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Moment matrices and real root finding

Author(s):

Ph. Rostalski
Conference/Journal:

MSRI Workshop on Algebraic Statistics, Berkeley, USA
Abstract:

The problem of determining the existence of a Borel measure, such that a given multi-sequence of real numbers agrees with its first few moments is known as the truncated moment problem. The main tool to analyze this question is the so called moment matrix, a positive semi-definite matrix with quasi-Hankel structure, whose entries consist of the given moments. We will analyze the algebraic structure of this matrix and show, how it can be turned into an algorithm for computing all real roots, or even all roots in a given semi-algebraic subset. The relation to certain global optimization relaxations based on sum-of-squares and moment matrices is also discussed and we will introduce a new and more efficient stopping criterion. This talk is based on the joined work with Monique Laurent (CWI) and Jean Lasserre (LAAS-CNRS).

Year:

2008
Type of Publication:

(06)Talk
Supervisor:

M. Morari

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