Krylov subspace methods

Krylov subspace methods are a group of mathematical techniques used to solve large systems of linear equations or find eigenvalues of matrices. They work by creating a sequence of approximations within a special space (the Krylov subspace) generated from the original problem and an initial guess. By leveraging this subspace, these methods efficiently focus on the most relevant information, allowing for faster convergence to the solution. They are widely used in scientific computing and engineering, especially for problems too complex for traditional methods to handle effectively.