A Spectral Projection Preconditioner for Solving Ill Conditioned Linear Systems
Provides a more efficient solver for ill-conditioned linear systems, which are common in scientific computing, but the improvements are incremental over existing preconditioned Krylov methods.
The paper introduces a spectral projection preconditioner combined with a deflated Krylov subspace method for ill-conditioned linear systems, achieving faster convergence and higher accuracy (e.g., fewer iterations and smaller error norms) compared to standard Krylov solvers.
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer iterations to achieve the convergence criterion for solving an ill conditioned problem than a Krylov subspace solver. In our numerical experiments, the solution obtained by the proposed algorithm is more accurate in terms of the norm of the distance to the exact solution of the linear system of equations.