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Numerical computation of the number of zeros of real polynomials in the open unit disk using a Chebyshev polynomials representation

✍ Scribed by B. Gleyse; A. Larabi

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 195 KB
Volume: 24
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2010.11.016

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✦ Synopsis

We present a general and efficient numerical method with low computational complexity for computing the number of zeros of a real polynomial in the unit disk.

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Algebraic computation of the number of zeros of a complex polynomial in the open unit disk by a polynomial representation

✍ B. Gleyse; A. Larabi; M. Moflih 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 224 KB

We present a general method for the exact computation of the number of zeros of a complex polynomial inside the unit disk, assuming that the polynomial does not vanish on the unit circle. We prove the existence of a polynomial sequence. This sequence involves a reduced number of arithmetic operation