Factorization of multivariate positive Laurent polynomials

Dedicated to Barry Simon on the occasion of his 60th birthday
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Abstract

Recently Dritschel proved that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Fejér–Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. Finally we discuss how to compute nonnegative Laurent polynomial factorizations in the multivariate setting.

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1

This author is partly supported by an NSF grant.

2

This author is partly supported by the National Science Foundation under grant EAR-0327577 and the School of Mathematics, at the Georgia Institute of Technology where he visited during the fall, 2004.