MATLAB Implementation of Gauss-Newton Optimization Algorithm

This document provides MATLAB source code for implementing the Gauss-Newton optimization algorithm. Below, I will provide detailed background information and application scenarios for this algorithm. The Gauss-Newton method is a nonlinear least-squares optimization technique primarily used for solving nonlinear data fitting problems. Its key advantages include robust handling of noisy data and excellent numerical stability. In practical applications, the Gauss-Newton algorithm is widely employed in fields such as image processing, signal processing, and machine learning. The MATLAB source code provided here offers a comprehensive implementation example of the Gauss-Newton optimization algorithm. Through this code, you can learn how to implement the Gauss-Newton method in MATLAB and apply it to your own data processing and analysis problems. The implementation demonstrates key components including: - Jacobian matrix calculation using finite differences or analytical derivatives - Iterative parameter updates using the formula: Δθ = -(JᵀJ)⁻¹Jᵀr - Residual computation and convergence criteria handling - Step size control and regularization techniques for numerical stability Furthermore, you can modify and optimize the code for different application scenarios by adjusting parameters such as convergence tolerance, maximum iteration count, and regularization parameters. The modular structure allows easy adaptation to various nonlinear fitting problems. In summary, this document provides a valuable tool for understanding and applying the Gauss-Newton optimization algorithm. The code includes comments explaining each computational step and offers practical insights into algorithm implementation. We wish you success in your practical applications!