Fixed Point Iteration Method for Solving Nonlinear Equation Systems

This program implements the fixed point iteration method in MATLAB for solving systems of nonlinear equations. The fixed point iteration method is an effective numerical analysis technique that iteratively approximates solutions to equations until specific convergence criteria are met. In this implementation, the algorithm transforms the nonlinear system into an equivalent fixed-point form and successively applies iteration functions to approach the solution. Key implementation features include: - Conversion of nonlinear equations to fixed-point form g(x) = x - Iterative updates using x_{k+1} = g(x_k) - Built-in convergence checking based on tolerance thresholds - Maximum iteration limits to prevent infinite loops Compared to other numerical methods, fixed point iteration typically requires less computational overhead, making it particularly suitable for handling complex nonlinear systems. The MATLAB environment provides optimized matrix operations and function handling, offering a convenient solution that saves significant time and effort in numerical computation. The implementation includes error handling and allows for customization of convergence parameters to adapt to different equation systems.