Abstract
We present variants of the block-GMRES(\(m\)) algorithms due to Vital and the block-LGMRES(\(m\),\(k\)) by Baker, Dennis and Jessup, obtained with replacing the standard QR factorization by a rank-revealing QR factorization in the Arnoldi process. The resulting algorithm allows for dynamic block deflation whenever there is a linear dependency between the Krylov vectors or the convergence of a right-hand-side occurs. \(\textsc{Fortran 90}\) implementations of the algorithms were tested on a number of test matrices and the results show that in some cases a substantial reduction of the execution time is obtained. Also a parallel implementation of our variant of the block-GMRES(\(m\)) algorithm, using \(\textsc{Fortran 90}\) and \(\textsc{MPI}\) was tested on \(\textsc{SunFire 15K}\) parallel computer, showing good parallel efficiency.
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This work was carried out while the author was at IM/UFRGS.
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da Cunha, R.D., Becker, D. Dynamic block GMRES: an iterative method for block linear systems. Adv Comput Math 27, 423–448 (2007). https://doi.org/10.1007/s10444-006-9012-5
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DOI: https://doi.org/10.1007/s10444-006-9012-5