### Abstract

For fitting curves or surfaces to observed or measured data, a common criterion is orthogonal distance regression. We consider here a natural generalization of a particular formulation of that problem which involves the replacement of least squares by the Chebyshev norm. For example, this criterion may be a more appropriate one in the context of accept/reject decisions for manufactured parts. The resulting problem has some interesting features: it has much structure which can be exploited, but generally the solution is not unique. We consider a method of Gauss-Newton type and show that if the non-uniqueness is resolved in a way which is consistent with a particular way of exploiting the structure in the linear subproblem, this can not only allow the method to be properly defined, but can permit a second order rate of convergence. Numerical examples are given to illustrate this.

Original language | English |
---|---|

Pages (from-to) | 443-461 |

Number of pages | 19 |

Journal | BIT Numerical Mathematics |

Volume | 45 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 |

### Keywords

- l∞ norm
- Curve fitting
- Non-unique solution
- Gauss-Newton method
- Simplex method

## Fingerprint Dive into the research topics of 'Fitting parametric curves and surfaces by l∞ distance regression'. Together they form a unique fingerprint.

## Cite this

Watson, A., & Al-Subaihi, I. (2005). Fitting parametric curves and surfaces by l∞ distance regression.

*BIT Numerical Mathematics*,*45*(3), 443-461. https://doi.org/10.1007/s10543-005-0018-z