Newton Iteration

Newton iteration, a fundamental iterative method for finding roots of functions, is seeing renewed interest across diverse fields. Current research focuses on improving its efficiency and robustness, particularly within machine learning (e.g., reinforcement learning, neural network training) and scientific computing (e.g., solving differential equations, optimization problems). This involves developing hybrid methods combining Newton iteration with other techniques like quasi-Newton methods, neural networks, and regularization to enhance convergence speed, handle high dimensionality, and address issues like stiffness and non-convexity. These advancements are impacting areas ranging from data privacy in distributed computing to accelerating simulations in computational fluid dynamics.