GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
A quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric systems
SIAM Journal on Scientific Computing
GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Scientific Computing
GBi-CGSTAB(s,L): IDR(s) with higher-order stabilization polynomials
Journal of Computational and Applied Mathematics
Bi-CGSTAB as an induced dimension reduction method
Applied Numerical Mathematics
Interpreting IDR as a Petrov-Galerkin Method
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)
Hi-index | 7.30 |
The IDR(s) method proposed by Sonneveld and van Gijzen is an effective method for solving nonsymmetric linear systems, but usually with irregular convergence behavior. In this paper, we reformulate the relations of residuals and their auxiliary vectors generated by the IDR(s) method in matrix form. Then, using this new formulation and motivated by other QMR-type methods, we propose a variant of the IDR(s) method, called QMRIDR(s), for overcoming the disadvantage of its irregular convergence behavior. Both fast and smooth convergence behaviors of the QMRIDR(s) method can be shown. Numerical experiments are reported to show the efficiency of our proposed method.