Chebyshev series expansion of inverse polynomials
Abstract
The Chebyshev series expansion of the inverse of a polynomial is well defined if the polynomial has no roots in [1,1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. Also, if the first k of the coefficients an are known, the others become linear combinations of these derived recursively from the bj's. On a closely related theme, finding a polynomial with minimum relative error towards a given f(x) is approximately equivalent to finding the bj in ; a Newton algorithm produces these if the Chebyshev expansion of f(x) is known.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 November 2006
 arXiv:
 arXiv:math/0403344
 Bibcode:
 2006JCoAM.196..596M
 Keywords:

 Chebyshev series;
 Orthogonal polynomials;
 Approximation;
 Mathematics  Classical Analysis and ODEs;
 33C45 (Primary);
 42C20;
 41A50 (Secondary)
 EPrint:
 LaTeX2e, 24 pages, 1 PostScript figure. More references. Corrected typos in (1.1), (3.4), (4.2), (A.5), (E.8) and (E.11)