Decomposition of perturbed Chebyshev polynomials

Authors:
Thomas Stoll
Affiliations:
Institute of Discrete Mathematics and Geometry, TU Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
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Abstract

We characterize polynomial decomposition f"n=r@?q with r,q@?C[x] of perturbed Chebyshev polynomials defined by the recurrencef"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 a0. These polynomials generalize the Chebyshev polynomials, which are obtained by setting a=14, 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 Grobner bases with Maple 10. Some additional data for the calculations are available on the author's web page.