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**On a fast convergence of the rational-trigonometric-polynomial interpolation.**
*(English)*
Zbl 1268.65019

Summary: We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate the convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to the Krylov-Lanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.

### MSC:

65D05 | Numerical interpolation |

41A05 | Interpolation in approximation theory |

65T40 | Numerical methods for trigonometric approximation and interpolation |

42A15 | Trigonometric interpolation |

41A10 | Approximation by polynomials |

### Keywords:

convergence acceleration; Krylov-Lanczos interpolation; rational correction functions; rational-trigonometric-polynomial interpolation; numerical experiments
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\textit{A. Poghosyan}, Adv. Numer. Anal. 2013, Article ID 315748, 13 p. (2013; Zbl 1268.65019)

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### References:

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