LM拟合matlab应用

### Levenberg-Marquardt Algorithm Fitting in MATLAB Example Tutorial

The Levenberg-Marquardt algorithm provides an effective approach for solving non-linear least squares problems. In MATLAB, this can be achieved using built-in functions such as `lsqcurvefit` or by implementing custom code that leverages optimization toolboxes.

#### Using Built-In Function lsqcurvefit

MATLAB's Optimization Toolbox offers the function `lsqcurvefit`, which supports specifying the 'levenberg-marquardt' method directly through its options parameter:

% Define model function y = f(x,p), where p contains parameters to fit.
fun = @(p,xdata) p(1)*exp(-p(2)*xdata);

% Initial guess for parameters
initialParams = [1; 0];

% Data points
xData = linspace(0, 4);
yData = fun([3, 2], xData) + randn(size(xData))*0.1;

options = optimoptions('lsqcurvefit', 'Algorithm', 'levenberg-marquardt');

[pOptimized, resnorm] = lsqcurvefit(fun, initialParams, xData, yData, [], [], options);
disp(['Optimized Parameters:', num2str(pOptimized')]);

This script demonstrates how one might apply LM fitting on exponential decay data with added Gaussian noise[^1].

For more complex models requiring manual implementation of gradients or Hessians, consider writing a dedicated objective function alongside setting up appropriate stopping criteria within the optimizer settings.