Iterative Methods
Iterative methods are computational algorithms used to solve mathematical problems, such as systems of linear equations, eigenvalue problems, or optimization tasks, by generating a sequence of progressively better approximations from an initial guess. They are fundamental in numerical analysis and scientific computing, often applied when direct methods are computationally infeasible or inefficient for large-scale problems. These methods rely on repeated refinement steps until a convergence criterion is met, making them essential for simulations, data analysis, and engineering applications.
Developers should learn iterative methods when working on problems involving large datasets, high-dimensional systems, or complex simulations where direct solutions are too slow or memory-intensive, such as in machine learning optimization, fluid dynamics, or financial modeling. They are crucial for implementing efficient algorithms in fields like computer graphics, physics engines, and data science, enabling scalable solutions that adapt to real-time constraints and iterative improvement processes.