Dynamic block GMRES: an iterative method for block linear systems,
da Cunha, R. D., and Becker D.
, 2007, Volume 27, Issue 4, p.423 - 448, (2007)
Abstractn/a
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.
A Parallel Implementation of the Restarted GMRES Iterative Method for Nonsymmetric Systems of Linear Equations,
da Cunha, R. D., and Hopkins T. R.
, Advances in Computational Mathematics, apr, Volume 2, Number 3, Basel, p.261–277, (1994)
AbstractAlso as TR-7-93, Computing Laboratory, University of Kent at Canterbury
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Parallel Preconditioned {Conjugate-Gradients} Methods on Transputer Networks,
da Cunha, R. D., and Hopkins T. R.
, Transputer Communications, Volume 1, Number 2, p.111–125, (1993)
AbstractAlso as TR-5-93, Computing Laboratory, University of Kent at Canterbury, U.K.
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