Abstract
For any trigonometric polynomial $\phi(\theta)$, we give a constructive algorithm by Sylvester elimination which produces matrices $C_1, C_2, C_3$ such that $\det(C_1+ \Re(\phi(\theta)) C_2+ \Im(\phi(\theta)) C_3)=0.$ For a typical trigonometric polynomial, we assert that $C_1$ is positive definite, and thus the typical polynomial curve admits
Citation
Mao-Ting Chien. Hiroshi Nakazato. "Determinantal representation of trigonometric polynomial curves via Sylvester method." Banach J. Math. Anal. 8 (1) 269 - 278, 2014. https://doi.org/10.15352/bjma/1381782099
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