Dynamic block GMRES: an iterative method for block linear systems

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. 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 Fortran 90 and MPI was tested on SunFire 15K parallel computer, showing good parallel efficiency.