Self-Developed Newton's Iteration Method Program for Solving Bivariate Quadratic Equations

This self-developed program solves bivariate quadratic equations using Newton's iteration method, a numerical computational technique that approximates function roots using first and second derivatives. The program implementation includes the following key components: The algorithm establishes a Jacobian matrix containing partial derivatives of the equation system, which is essential for the iterative convergence process. The program executes these main steps: 1. Input equation coefficients and customizable iteration steps - users can define parameters like maximum iterations and convergence tolerance to balance computational efficiency and solution accuracy 2. Compute equation solutions through Newton's iteration method - the core algorithm involves calculating the inverse of the Jacobian matrix and updating solution estimates iteratively until convergence criteria are met 3. Output solution results with precision metrics - the program displays final solutions, iteration count, and residual errors for verification Through this implementation, users can gain deeper understanding of Newton's method principles and applications in numerical analysis. By adjusting iteration parameters, users can control computational efficiency and solution precision, observing how step size affects convergence behavior in nonlinear equation systems.