### Abstract

We consider the case that a function with large gradients in the interior of an interval has to be approximated over this interval or that the pseudospectral method is used to compute a similar solution of an ordinary boundary value problem. In both cases we assume that the function has minimal continuity properties but can be evaluated anywhere in the given interval. The key idea is then to attach poles to the polynomial interpolant, respectively solution of the collocation problem to obtain a special rational function with poles whose location has been optimized suitably. In the first case, the max norm of the error is minimized while in the second, the same norm is minimized of the residual of the given differential equation. The algorithms are presented and discussed. Their effectiveness is demonstrated with numerical results.

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

Pages (from-to) | 527-544 |

Number of pages | 18 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 32 |

Issue number | 2 |

State | Published - Jun 2002 |

### Fingerprint

### Keywords

- Linear rational collocation
- Linear rational interpolation
- Pole optimization

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Rocky Mountain Journal of Mathematics*,

*32*(2), 527-544.

**Linear rational interpolation and its application in approximation and boundary value problems.** / Berrut, Jean Paul; Mittelmann, Hans.

Research output: Contribution to journal › Article

*Rocky Mountain Journal of Mathematics*, vol. 32, no. 2, pp. 527-544.

}

TY - JOUR

T1 - Linear rational interpolation and its application in approximation and boundary value problems

AU - Berrut, Jean Paul

AU - Mittelmann, Hans

PY - 2002/6

Y1 - 2002/6

N2 - We consider the case that a function with large gradients in the interior of an interval has to be approximated over this interval or that the pseudospectral method is used to compute a similar solution of an ordinary boundary value problem. In both cases we assume that the function has minimal continuity properties but can be evaluated anywhere in the given interval. The key idea is then to attach poles to the polynomial interpolant, respectively solution of the collocation problem to obtain a special rational function with poles whose location has been optimized suitably. In the first case, the max norm of the error is minimized while in the second, the same norm is minimized of the residual of the given differential equation. The algorithms are presented and discussed. Their effectiveness is demonstrated with numerical results.

AB - We consider the case that a function with large gradients in the interior of an interval has to be approximated over this interval or that the pseudospectral method is used to compute a similar solution of an ordinary boundary value problem. In both cases we assume that the function has minimal continuity properties but can be evaluated anywhere in the given interval. The key idea is then to attach poles to the polynomial interpolant, respectively solution of the collocation problem to obtain a special rational function with poles whose location has been optimized suitably. In the first case, the max norm of the error is minimized while in the second, the same norm is minimized of the residual of the given differential equation. The algorithms are presented and discussed. Their effectiveness is demonstrated with numerical results.

KW - Linear rational collocation

KW - Linear rational interpolation

KW - Pole optimization

UR - http://www.scopus.com/inward/record.url?scp=0036624951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036624951&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036624951

VL - 32

SP - 527

EP - 544

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 2

ER -