Cyclic reduction, dichotomy and the estimation of differential equations

Research Report MRR96-051

Cyclic reduction, dichotomy and the estimation of differential equations

M.R.Osborne

Abstract: In the estimation of ordinary differential equations given observed data it is necessary to parametrize the solutions in a computationally tractable way in order to make comparisons with the given data. Typically this is done by adjoining initial or boundary conditions, and this requires additional information on the solution structure in order to do this in a manner that leads to stable computation of the comparison solutions. Here, cyclic reduction is used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints. If orthogonal transformations are used in the cyclic reduction process then it appears that stable computations are possible without the need for the structural information needed to devise the stable imbeddings. The process produces a new representation of the solutions of the ODE system, and this is described.

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