Gauss-Newton method, nonlinear least-squares

Kinetic curves were analyzed and the further correlations were determined with a nonlinear least-square-method PC program, working with the Gauss-Newton method. 

Least-squares methods are usually used for fitting a model to experimental data. They may be used for functions consisting of square sums of nonlinear functions. The well-known Gauss-Newton method often leads to instabilities in the minimization process since the steps are too large. The Marquardt algorithm [9 1 is better in this respect but it is computationally expensive. 

In general, the error e tic-q-i+j, 0) is a non-linear function of the parameter vector 0. Therefore, the above problem is a well-known nonlinear least squares problem (NLSP) that may be solved by various optimisation algorithms such as the Levenberg-Marquardt algorithm [2], the quasi-Newton method or the Gauss-Newton (GN) algorithm [3]. 

Linear and nonlinear regression analyses, including least squares, estimated vector of parameters, method of steepest descent, Gauss-Newton method, Marquardt Method, Newton Method,... 

Least squares multiple nonlinear regression using the Marquardt and Gauss-Newton methods. The program can fit simultaneous ordinary differential equations and/or algebraic equations to multiresponse data. 

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