### Abstract

After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.

Original language | English (US) |
---|---|

Pages (from-to) | 315-328 |

Number of pages | 14 |

Journal | Numerical Algorithms |

Volume | 23 |

Issue number | 4 |

State | Published - 2000 |

### Fingerprint

### Keywords

- Interpolation
- Optimal interpolation
- Rational interpolation

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Numerical Algorithms*,

*23*(4), 315-328.

**Rational interpolation through the optimal attachment of poles to the interpolating polynomial.** / Berrut, Jean Paul; Mittelmann, Hans.

Research output: Contribution to journal › Article

*Numerical Algorithms*, vol. 23, no. 4, pp. 315-328.

}

TY - JOUR

T1 - Rational interpolation through the optimal attachment of poles to the interpolating polynomial

AU - Berrut, Jean Paul

AU - Mittelmann, Hans

PY - 2000

Y1 - 2000

N2 - After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.

AB - After recalling some pitfalls of polynomial interpolation (in particular, slopes limited by Markov's inequality) and rational interpolation (e.g., unattainable points, poles in the interpolation interval, erratic behavior of the error for small numbers of nodes), we suggest an alternative for the case when the function to be interpolated is known everywhere, not just at the nodes. The method consists in replacing the interpolating polynomial with a rational interpolant whose poles are all prescribed, written in its barycentric form as in [4], and optimizing the placement of the poles in such a way as to minimize a chosen norm of the error.

KW - Interpolation

KW - Optimal interpolation

KW - Rational interpolation

UR - http://www.scopus.com/inward/record.url?scp=0034390542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034390542&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034390542

VL - 23

SP - 315

EP - 328

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

IS - 4

ER -