SIAM Journal on Matrix Analysis and Applications
Nested Krylov methods based on GCR
Journal of Computational and Applied Mathematics
Global FOM and GMRES algorithms for matrix equations
Applied Numerical Mathematics
Truncation Strategies for Optimal Krylov Subspace Methods
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Block Iterative Solver for Complex Non-Hermitian Systems Applied to Large-Scale, Electronic-Structure Calculations
The block Lanczos method for linear systems with multiple right-hand sides
Applied Numerical Mathematics
Skew-symmetric methods for nonsymmetric linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
A Simplified and Flexible Variant of GCROT for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Flexible GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
SIAM Journal on Scientific Computing
A block IDR(s) method for nonsymmetric linear systems with multiple right-hand sides
Journal of Computational and Applied Mathematics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Flexible Variants of Block Restarted GMRES Methods with Application to Geophysics
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
This study is mainly focused on iterative solution to multiple linear systems with several right-hand sides. For solving such systems efficiently, we explore a new block GCROT(m,k) (BGCROT(m,k)) method, which is derived by extending GCROT(m,k) method [Jason E. Hicken, David W. Zingg, A simplified and flexible variant of GCROT for solving nonsymmetric linear systems, SIAM J. Sci. Comput. 32 (2010) 1672-1694]. We analyze its main properties. It is shown that under the condition of full rank of block residual, the Frobenius norm of the block residual generated by the proposed method is always nonincreasing. Moreover, we also present its block flexible version, BFGCROT(m,k). Finally, numerical examples demonstrate that the BGCROT(m,k) method and its flexible variant can achieve a smoothed residual and can be more competitive than some other block solvers.