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448</style></pages><isbn><style face="normal" font="default" size="100%">1572-9044</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Parallel Implementation of the Restarted GMRES Iterative Method for Nonsymmetric Systems of Linear Equations</style></title><secondary-title><style face="normal" font="default" size="100%">Advances in Computational Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1994</style></year><pub-dates><date><style  face="normal" font="default" size="100%">apr</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">3</style></number><publisher><style face="normal" font="default" size="100%">J.C. Baltzer</style></publisher><pub-location><style face="normal" font="default" size="100%">Basel</style></pub-location><volume><style face="normal" font="default" size="100%">2</style></volume><pages><style face="normal" font="default" size="100%">261–277</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;Also as TR-7-93, Computing Laboratory, University of Kent at Canterbury&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Using Parallel Programming Environments on Clusters of Workstations</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year><pub-dates><date><style  face="normal" font="default" size="100%">nov</style></date></pub-dates></dates><publisher><style face="normal" font="default" size="100%">Computing Laboratory, University of Kent at Canterbury</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><work-type><style face="normal" font="default" size="100%">Internal Report 12-93</style></work-type><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Parallel Implementation of the Restarted GMRES Iterative Method for Nonsymmetric Systems of Linear Equations</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year><pub-dates><date><style  face="normal" font="default" size="100%">apr</style></date></pub-dates></dates><publisher><style face="normal" font="default" size="100%">Computing Laboratory, University of Kent at Canterbury</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><work-type><style face="normal" font="default" size="100%">TR-7-93</style></work-type><notes><style face="normal" font="default" size="100%">&lt;p&gt;Also in: {\em Advances in Computational Mathematics}, 2(3):261-277, J.C. Baltzer, April 1994&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Porting Linear Algebra Subroutines From Transputers To Clusters of Workstations</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year><pub-dates><date><style  face="normal" font="default" size="100%">apr</style></date></pub-dates></dates><publisher><style face="normal" font="default" size="100%">Computing Laboratory, University of Kent at Canterbury</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><work-type><style face="normal" font="default" size="100%">TR-6-93</style></work-type><notes><style face="normal" font="default" size="100%">&lt;p&gt;Also in: Proceedings of the ``World Transputer Congress'' conference, September 20–22, 1993, Aachen, V.1, pp. 660-667&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Parallel Preconditioned {Conjugate-Gradients} Methods on Transputer Networks</style></title><secondary-title><style face="normal" font="default" size="100%">Transputer Communications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><number><style face="normal" font="default" size="100%">2</style></number><volume><style face="normal" font="default" size="100%">1</style></volume><pages><style face="normal" font="default" size="100%">111–125</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;Also as TR-5-93, Computing Laboratory, University of Kent at Canterbury, U.K.&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The Parallel Solution of Partial Differential Equations on Transputer Networks</style></title><tertiary-title><style face="normal" font="default" size="100%">Transputing for Numerical and Neural Network Applications</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><publisher><style face="normal" font="default" size="100%">IOS Press</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam</style></pub-location><pages><style face="normal" font="default" size="100%">96–109</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;Also as TR-17-92, Computing Laboratory, University of Kent at Canterbury, U.K.&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">da Cunha, R. D.</style></author><author><style face="normal" font="default" size="100%">Hopkins, T. R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The Parallel Solution of Systems of Linear Equations Using Iterative Methods on Transputer Networks</style></title><tertiary-title><style face="normal" font="default" size="100%">Transputing for Numerical and Neural Network Applications</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><publisher><style face="normal" font="default" size="100%">IOS Press</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam</style></pub-location><pages><style face="normal" font="default" size="100%">1–13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;Also as TR-16-92, Computing Laboratory, University of Kent at Canterbury, U.K.&lt;/p&gt;
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