arXiv math/05031332005-03-07math.CA

Factorization of Multivariate Positive Laurent Polynomials

Jeffrey S. Geronimo, Ming-Jun Lai

英文摘要：

Recently Dritschel proves 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 Fejer-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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