GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Matrix computations (3rd ed.)
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Breakdown-free GMRES for Singular Systems
SIAM Journal on Matrix Analysis and Applications
Tikhonov regularization based on generalized Krylov subspace methods
Applied Numerical Mathematics
FGMRES for linear discrete ill-posed problems
Applied Numerical Mathematics
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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.