Factorization of Multivariate Positive Laurent Polynomials
Classical Analysis and ODEs
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0503133,
title = {Factorization of Multivariate Positive Laurent Polynomials},
author = {Jeffrey S. Geronimo and Ming-Jun Lai},
journal= {arXiv preprint arXiv:math/0503133},
year = {2007}
}