Fitting Systems of Linear Differential Equations Using Computer Generated Exact Derivatives

Publisher Website
Google Scholar
Abstract
The problem of estimating coefficients and initial values in a system of linear differential equations from observations on linear combinations of the system's responses is addressed. Using the Gauss-Newton algorithm, the reqllired function values are obtained by expressing the system's solution in terms of the eigenvalues and eigenvectors of its coefficient matrix aud its initial values. Differentiating this solution gives expressious for the required function derivatives in terms of these same eigenvalues and eigenvectors. The advantage of this approach is that it, uses exact analytic expressions for the required function values and derivatives rather than resorting to numerical integration or secants. An application to compartment, analysis is considered aud results are compared with those obtained by using the SAAM program of Berman and Weiss.

This publication has 0 references indexed in Scilit: