Kaczmarz Algorithm

The Kaczmarz algorithm is an iterative method for solving large-scale linear systems, particularly useful when dealing with noisy data or high-dimensional problems. Current research focuses on extending its capabilities through variations like randomized Kaczmarz, incorporating regularization techniques (e.g., ℓ₁-norm), and adapting it for distributed and adversarial settings, including applications in tensor recovery and neural network optimization. These advancements enhance the algorithm's efficiency and robustness, impacting diverse fields such as machine learning, signal processing, and scientific computing by providing faster and more reliable solutions to complex linear problems.