# Guaranteed Parameter Set Estimation for Exponential Sums: The Three-Terms Case

Guaranteed Parameter Set Estimation for Exponential Sums: The Three-Terms Case In this paper the problem of parameter estimation for exponential sums with three terms is considered. This task consists of finding the set of parameters (amplitudes as well as decay constants) such that the exponential sum attains values in specified intervals at prescribed time data points. These intervals represent uncertainties in the measurements. An interval variant of Prony’s method is given by which intervals can be found containing all the consistent values of the respective parameters. By the use of interval arithmetic these enclosures can also be guaranteed in the presence of rounding errors. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Guaranteed Parameter Set Estimation for Exponential Sums: The Three-Terms Case

, Volume 13 (4) – Jun 2, 2007
9 pages

/lp/springer_journal/guaranteed-parameter-set-estimation-for-exponential-sums-the-three-Ckk6RF1mR2
Publisher
Subject
Mathematics; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Approximations and Expansions; Computational Mathematics and Numerical Analysis
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-007-9034-9
Publisher site
See Article on Publisher Site

### Abstract

In this paper the problem of parameter estimation for exponential sums with three terms is considered. This task consists of finding the set of parameters (amplitudes as well as decay constants) such that the exponential sum attains values in specified intervals at prescribed time data points. These intervals represent uncertainties in the measurements. An interval variant of Prony’s method is given by which intervals can be found containing all the consistent values of the respective parameters. By the use of interval arithmetic these enclosures can also be guaranteed in the presence of rounding errors.

### Journal

Reliable ComputingSpringer Journals

Published: Jun 2, 2007

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