### Abstract

Let x_{0},...,x_{N} be N + 1 interpolation points (nodes) and f_{0},...,f_{N} be N + 1 interpolation data. Then every rational function r with numerator and denominator degrees ≤N interpolating these values can be written in its barycentric form r(x) = ∑^{N}_{k=0}u_{k}/x - x_{k}f_{k}/∑^{N}_{k=0}u_{k}/x - x_{k}, which is completely determined by a vector u of N + 1 barycentric weights u_{k}. Finding u is therefore an alternative to the determination of the coefficients in the canonical form of r; it is advantageous inasmuch as u contains information about unattainable points and poles. In classical rational interpolation the numerator and the denominator of r are made unique (up to a constant factor) by restricting their respective degrees. We determine here the corresponding vectors u by applying a stabilized elimination algorithm to a matrix whose kernel is the space spanned by the u's. The method is of complexity script O sign(n^{3}) in terms of the denominator degree n; it seems on the other hand to be among the most stable ones.

Original language | English (US) |
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Pages (from-to) | 355-370 |

Number of pages | 16 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 78 |

Issue number | 2 |

DOIs | |

State | Published - Feb 17 1997 |

### Keywords

- Barycentric representation
- Barycentric weights
- Interpolation
- Rational interpolation

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics