MATLAB Implementation of Newton's Iteration Method

This MATLAB source code implements Newton's iteration method for solving equation systems. Newton's iteration method is a numerical computational technique used to find roots of functions or solutions to equation systems. In this implementation, the method handles both linear and nonlinear equation systems through an iterative approximation process that utilizes function derivatives to converge toward solutions. The code employs MATLAB's matrix operations and symbolic differentiation capabilities to compute Jacobian matrices efficiently. Key implementation aspects include: - Function handle implementation for system equations - Automatic Jacobian calculation using finite differences or symbolic math - Convergence criteria based on tolerance thresholds and maximum iteration limits - Error handling for singularity conditions and divergence cases The algorithm works by starting with an initial guess and iteratively refining the solution using the formula: x_{n+1} = x_n - J(x_n)^{-1} * F(x_n), where J is the Jacobian matrix and F is the system function. This implementation includes safeguards for numerical stability and provides detailed convergence monitoring. This code serves as a practical reference for implementing Newton's method in MATLAB, featuring modular design that allows easy adaptation to different equation systems while maintaining computational efficiency.