Iterative Solvers
Iterative solvers are numerical algorithms used to solve large systems of linear equations, such as Ax = b, by starting with an initial guess and refining it through successive approximations until convergence. They are particularly valuable for sparse matrices where direct methods like Gaussian elimination become computationally expensive or infeasible. Common examples include the Conjugate Gradient method, GMRES, and Jacobi iteration.
Developers should learn iterative solvers when working on scientific computing, engineering simulations, or machine learning problems that involve large-scale linear systems, as they offer memory efficiency and scalability compared to direct solvers. They are essential in fields like computational fluid dynamics, finite element analysis, and optimization algorithms where matrices are often sparse and high-dimensional.