Factorization of multivariate positive Laurent polynomials |
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Authors: | Jeffrey S. Geronimo Ming-Jun Lai |
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Affiliation: | aSchool of Mathematics, The Georgia Institute of Technology, Atlanta, GA 30332, USA;bDepartment of Mathematics, The University of Georgia, Athens, GA 30602, USA |
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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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