On the Convergence of Polynomial Approximation of Rational Functions

@article{Wang1997OnTC,
  title={On the Convergence of Polynomial Approximation of Rational Functions},
  author={Guo-jin Wang and Thomas W. Sederberg and Falai Chen},
  journal={Journal of Approximation Theory},
  year={1997},
  volume={89},
  pages={267-288}
}
This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certainr×rmatrix are less than 2, whereris the degree of the rational function (or curve), and where the elements of the matrix are expressions involving only the denominator polynomial coefficients (weights) of… Expand

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