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TitleDecomposition of perturbed Chebyshev polynomials
Author(s) Stephan Thomasse
TypeArticle in Journal
AbstractWe characterize polynomial decomposition f n = r ∘ q with r , q ∈ C [ x ] of perturbed Chebyshev polynomials defined by the recurrence f 0 ( x ) = b , f 1 ( x ) = x - c , f n + 1 ( x ) = ( x - d ) f n ( x ) - af n - 1 ( x ) , n ⩾ 1 , where a , b , c , d ∈ R and a > 0 . These polynomials generalize the Chebyshev polynomials, which are obtained by setting a = 1 4 , c = d = 0 and b ∈ 1 , 2 . At the core of the method, two algorithms for polynomial decomposition are provided, which allow to restrict the investigation to the resolution of six systems of polynomial equations in three variables. The final task is then carried out by the successful computation of reduced Gröbner bases with Maple 10. Some additional data for the calculations are available on the author
KeywordsCo-recursive and co-dilated orthogonal polynomials, Chebyshev polynomials, Polynomial decomposition, Gröbner bases
ISSN0377-0427
URL http://www.sciencedirect.com/science/article/pii/S037704270700132X
LanguageEnglish
JournalJournal of Computational and Applied Mathematics
Volume214
Number2
Pages356 - 370
Year2008
Edition0
Translation No
Refereed No
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