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Parameter estimation of ordinary differential equations

Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/6600

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Title: Parameter estimation of ordinary differential equations
Related: IMA journal of numerical analysis, Vol. 25, Issue 2, p. 264-285
DOI: 10.1093/imanum/drh016
Publisher: Oxford University Press
Date: 2005
Author/Creator: Li, Zhengfeng
Author/Creator: Osborne, Michael R
Author/Creator: Prvan, Tania
Description: This paper addresses the development of a new algorithm for parameter estimation of ordinary differential equations. Here, we show that (1) the simultaneous approach combined with orthogonal cyclic reduction can be used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints without the need for structural information to devise a stable embedding in the case of non-trivial dichotomy and (2) the Newton approximation of the Hessian information of the Lagrangian function of the estimation problem should be used in cases where hypothesized models are incorrect or only a limited amount of sample data is available. A new algorithm is proposed which includes the use of the sequential quadratic programming (SQP) Gauss–Newton approximation but also encompasses the SQP Newton approximation along with tests of when to use this approximation. This composite approach relaxes the restrictions on the SQP Gauss–Newton approximation that the hypothesized model should be correct and the sample data set large enough. This new algorithm has been tested on two standard problems.
Description: 22 page(s)
Subject Keyword: ordinary differential equations
Subject Keyword: data fitting
Subject Keyword: parameter estimation
Subject Keyword: orthogonal cyclic reduction
Subject Keyword: constrained optimization
Subject Keyword: SQP methods
Subject Keyword: Gauss–Newton approximation
Resource Type: journal article
Organisation: Macquarie University. Dept. of Statistics

Identifier: http://hdl.handle.net/1959.14/6600
Identifier: ISSN:0272-4979
Identifier: mq-rm-2005000013
Language: eng
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