Nonlinear Least Squares Curve Fitting

Summary There is no general solution for the minimization of chi-squared to find the best estimates of the parameters when the model is nonlinear. A number of methods have been developed that can often find the best estimates and their uncertainties with arbitrary precision. Iterative methods are usually used to minimize a nonlinear chi-squared. Another…

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Generalized Linear Least Squares Curve Fitting

Summary Least squares curve fitting can be generalized to work with any linear model to determine unique parameter estimates and uncertainties in terms of matrix equations. Linear models follow a general form. All other models are classified as nonlinear. While nonlinear models do not have a general analytic solution, some nonlinear models can be transformed…

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Linear Least Squares Curve Fitting of Straight Line Models

Summary Curve fitting is a useful procedure for testing theoretical models and estimating model parameters and their uncertainties. Curve fitting is carried out by choosing the set of estimated parameters that minimize an error function. The conventional error function for analytic results with calculus is the sum of the squares of residuals. The residuals are…

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