MATLAB Implementation of the Levenberg-Marquardt Algorithm with Custom Code

This content references a custom MATLAB program based on the Levenberg-Marquardt (LM) algorithm, though specific applications or implementation methods are not detailed initially. To improve understanding, we will elaborate on the program's implementation and design approach, along with its application scenarios and advantages. The implementation involves constructing the LM algorithm manually, which includes key steps such as calculating the Jacobian matrix, adjusting the damping parameter, and solving the regularized normal equations. This approach allows flexibility in handling nonlinear least-squares problems, common in fields like curve fitting and optimization. Additionally, relevant theoretical knowledge will be introduced, including background and current research in areas such as natural language processing and machine learning, to help readers appreciate the program's value and significance. For instance, the LM algorithm is widely used in training neural networks and optimizing model parameters, making this custom implementation a practical tool for experimentation and education.