## Abstract

We describe a systematic approach to the recovery of a function analytic in the upper half-plane, C^{+}, from measurements over a finite interval on the real axis, D ⊂ R. Analytic continuation problems of this type are well known to be ill-posed. Thus, the best one can hope for is a simple, linear procedure which exposes this underlying difficulty and solves the problem in a least-squares sense. To accomplish this, we first construct an explicit analytic approximation of the desired function and recast the continuation problem in terms of a 'residual function' defined on the measurement window D itself. The resulting procedure is robust in the presence of noise, and we demonstrate its performance with some numerical experiments.

Original language | English (US) |
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Pages (from-to) | 1307-1320 |

Number of pages | 14 |

Journal | Inverse Problems |

Volume | 17 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2001 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics