Chebyshev series expansion of inverse polynomials
@article{Mathar2006ChebyshevSE, title={Chebyshev series expansion of inverse polynomials}, author={R. Mathar}, journal={Journal of Computational and Applied Mathematics}, year={2006}, volume={196}, pages={596-607} }
The Chebyshev series expansion Σn=0∞anTn(x) of the inverse of a polynomial Σj=0kbjTj(x) 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… CONTINUE READING
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References
SHOWING 1-10 OF 60 REFERENCES
The minimality properties of chebyshev polynomials and their lacunary series
- Computer Science
- Numerical Algorithms
- 2008
- 1
Some estimates of the coefficients in the Chebyshev series expansion of a function
- Mathematics
- 1965
- 20
- PDF
The determination of the Chebyshev approximating polynomial for a differentiable function
- Mathematics
- 1959
- 21
- PDF
Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. Part I. Maehly type approximants
- Mathematics, Computer Science
- Numerical Algorithms
- 2008
- 9
The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function
- Mathematics
- 1964
- 84
- PDF
A Chebyshev polynomial method for line integrals with singularities
- Mathematics, Computer Science
- Adv. Comput. Math.
- 1999
- 2