Non-linear least-squares parameter estimation methods {steepest descent method} {method of steepest descent} can use points, far from minimum, where first derivative is maximum.
Methods {normal equations method} {method of normal equations} can find function minimum.
Non-linear least-squares parameter estimation methods {inverse-Hessian method} can use points near minimum, where first derivative equals zero.
Non-linear least-squares parameter estimation methods {Levenberg-Marquardt method} {Marquardt method} can generalize normal-equations method to find minimum and avoid steepest-descent and inverse-Hessian extremes.
Taking gradient by differentiating eliminates equation constants and so cannot calculate equation-constant magnitude. However, Hessian-matrix components can indicate constant magnitude.
Using scale factor can transform matrix into diagonally dominant matrix. After finding minimum, set scale factor to zero, and compute estimated fitted-parameter standard-error covariance matrix.
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Date Modified: 2022.0225