Parameter Estimation in Systems of Nonlinear Equations

K. Schittkowski: Numerische Mathematik, Vol. 68, 129-142 (1994)
Abstract: A numerical method is presented to determine parameters in a system of nonlinear equations in the following sense: Proceeding from given experimental data, e.g., observation times and measurements, the minimum least-squares distance of the measured data from a fitting criterion depending on the solution of a system of nonlinear equations is to be computed. Specifically coupled mass equilibrium models are described in more detail that are used in pharmaceutical applications for receptor-ligand binding studies. They are used for instance for the radioimmunological determination of Fenoterol or related substances. Numerical results based on laboratory data are included to test the robustness of the algorithm implemented.

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