Topics in Model Building. Part II. On Nonlinear Least Squares.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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Gauss suggested that, when the model is a nonlinear function of parameters, least square parameter estimates might be obtained by iterative linearization. To prevent difficulties in convergence, Levenberg, and later Marquardt, proposed a constrained minimization procedure. On critically examining this method with a linearly invariant metric for the parameters, the authors find this to be equivalent to a simple modification of the Gauss method which had been proposed earlier. Procedures to decide how far one should go along the Gauss solution vector are introduced which use only quantities already computed. Author
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