Fitting Systems of Linear Differential Equations Using Computer Generated Exact Derivatives

Article

Jennrich, Robert I.; Bright, Peter B.   (1976, ASQC and the American Statistical Association)   University of California, Los Angeles, CA

Technometrics    Vol. 18    No. 4
QICID: 8695    November 1976    pp. 385-392
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Article Abstract

The following paper with its discussion was the second of two invited papers presented in the Technometrics Session of the 136th Annual Meeting of the American Statistical Association held at Boston, August 23-27, 1976.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 required function values are obtained by expressing the system's solution in terms of the eigenvalues and eigenvectors of its coefficient matrix and its initial values. Differentiating this solution gives expressions 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 and result are compared with those obtained by using the SAAM program of Berman and Weiss.

Keywords

Regression,Differential equations,Analysis,Statistical methods


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