Decomposition methods for large linear discrete ill-posed problems

The solution of large linear discrete ill-posed problems by iterative methods continues to receive considerable attention. This paper presents decomposition methods that split the solution space into a Krylov subspace that is determined by the iterative method and an auxiliary subspace that can be chosen to help represent pertinent features of the solution. Decomposition is well suited for use with the GMRES, RRGMRES, and LSQR iterative schemes.