CMA Research Report
MRR02-001
Zhengfeng Li, Michael R. Osborne and Tania Prvan
Parameter Estimation of Ordinary Differential Equations
Abstract:
This paper addresses the development of a
new algorithm for the parameter estimation problems of ordinary
differential equations. Here,
we show that:
(1) the simultaneous approach combined with the
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 the structural information to
devise a stable imbeddings;
(2) the Newton approximation of the Hessian information of the
Lagrangian function of the estimation problem should be used in cases
where hypothesised models are incorrect or only a limited amount of
sample data
is available.
A new algorithm is proposed. Our new algorithm
includes the use of the SQP Gauss-Newton approximation but also
encompasses the SQP Newton approximation along with tests of when
to use this approximation. This relaxes the restrictions on the
SQP Gauss-Newton approximation that the hypothesised model should be
correct
and the sample data set large enough. This new algorithm has been
tested on two standard problems.
AMS Classification:
65F15
Date:
21 January 2002
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