GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Breakdown-free GMRES for Singular Systems
SIAM Journal on Matrix Analysis and Applications
MIQR: A Multilevel Incomplete QR Preconditioner for Large Sparse Least-Squares Problems
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
The Generalized Conjugate Residual (GCR) method with a variable preconditioning is an efficient method for solving a large sparse linear system Ax=b. It has been clarified by some numerical experiments that the Successive Over Relaxation (SOR) method is more effective than Krylov subspace methods such as GCR and ILU(0) preconditioned GCR for performing the variable preconditioning. However, SOR cannot be applied for performing the variable preconditioning when solving such linear systems that the coefficient matrix has diagonal entries of zero or is not square. Therefore, we propose a type of the generalized SOR (GSOR) method. By numerical experiments on the singular linear systems, we demonstrate that the variable preconditioned GCR using GSOR is effective.