# I would like to know which is the correct Trust-region method description adopted in the curve fitting toolbox

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Gaetano Mannino el 14 de Mzo. de 2023
Respondida: Shubham el 3 de Mayo de 2023
Here it's possible to find different subdescriptions of the Trust-region method:
while in the Curve Fitting Toolbox User's Guide is possible to find a brief description at page 141 of the pdf.
What is the correct mathematical description of the implemented algorithm adopted by curve fitting toolbox?
Thank you
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Shubham el 3 de Mayo de 2023
Hi Gaetano,
The Curve Fitting Toolbox is a software package that provides a collection of tools for fitting curves and surfaces to data.
One of the most used algorithms in the Curve Fitting Toolbox is the Levenberg-Marquardt algorithm, which is an iterative method for solving nonlinear least-squares problems. The algorithm works by minimizing the sum of the squares of the differences between the predicted values and the actual values of the data.
The mathematical description of the Levenberg-Marquardt algorithm involves updating the model’s parameters iteratively using a combination of the Gauss-Newton method and the steepest descent method. At each iteration, the algorithm computes a step size that minimises the objective function, which is the sum of the residuals' squares between the predicted and actual values. The step size is determined by solving a linear system of equations that involves the Jacobian matrix, which is the matrix of partial derivatives of the model with respect to the parameters.
Overall, the Curve Fitting Toolbox uses various algorithms for curve fitting, including the Levenberg-Marquardt algorithm and other methods such as the trust-region reflective algorithm, the Bayesian optimiser, and the genetic algorithm. The specific algorithm used depends on the type of data, the desired fit, and the options the user selects.
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