GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
An Implementation of the GMRES Method Using QR Factorization
Proceedings of the Fifth SIAM Conference on Parallel Processing for Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A new implementation of the CMRH method for solving dense linear systems
Journal of Computational and Applied Mathematics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
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This paper presents an implementation of the CMRH (Changing Minimal Residual method based on the Hessenberg process) iterative method suitable for parallel architectures. CMRH is an alternative to GMRES and QMR, the well-known Krylov methods for solving linear systems with non-symmetric coefficient matrices. CMRH generates a (non orthogonal) basis of the Krylov subspace through the Hessenberg process. On dense matrices, it requires less storage than GMRES. Parallel numerical experiments on a distributed memory computer with up to 16 processors are shown on some applications related to the solution of dense linear systems of equations. A comparison with the GMRES method is also provided on those test examples.