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## Abstract

This paper provides an error analysis of the three-term recurrence relation (TTRR) T n+1(x)=2x T n (x)−T n−1(x) for the evaluation of the Chebyshev polynomial of the first kind T N (x) in the interval [−1,1]. We prove that the computed value of T N (x) from this recurrence is very close to the exact value of the Chebyshev polynomial T N of a slightly perturbed value of x. The lower and upper bounds for the function CN(x)=|TN(x)|+|xT′N(x)| are also derived. Numerical examples that illustrate our theoretical results are given.

Original language | English |
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Pages (from-to) | 785-794 |

Number of pages | 10 |

Journal | Numerical Algorithms |

Volume | 69 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Aug 2015 |

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## Projects

- 1 Finished