GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational and Applied Mathematics
Greville's method for preconditioning least squares problems
Advances in Computational Mathematics
Hi-index | 7.30 |
We propose to precondition the GMRES method by using the incomplete Givens orthogonalization (IGO) method for the solution of large sparse linear least-squares problems. Theoretical analysis shows that the preconditioner satisfies the sufficient condition that can guarantee that the preconditioned GMRES method will never break down and always give the least-squares solution of the original problem. Numerical experiments further confirm that the new preconditioner is efficient. We also find that the IGO preconditioned BA-GMRES method is superior to the corresponding CGLS method for ill-conditioned and singular least-squares problems.