Iterative Solver

Iterative solvers are computational methods used to approximate solutions to complex mathematical problems, particularly large systems of equations, by repeatedly refining an initial guess. Current research emphasizes improving solver efficiency and accuracy through techniques like incorporating neural networks (e.g., using neural operators or deep learning for preconditioner design), combining machine learning with traditional methods (hybrid iterative solvers), and developing novel algorithms tailored to specific problem structures (e.g., sparsity-constrained optimization). These advancements are crucial for accelerating simulations across diverse fields, from scientific computing (solving partial differential equations) to engineering applications (e.g., additive manufacturing), enabling faster and more accurate solutions to previously intractable problems.