Effects due to the prEsence of charged dust particles on the growth rate of instabilities of low frequency electromagnetic waves propagating along the ambient magnetic field are investigated, using a kinetic theory which takes into account the collisional charging of the dust particles. For perpendicular ion temperature larger than the parallel ion temperature the dustless Plasma features the proton cyclotron anisotropy instability, which is gradually reduced by the prEsence of the dust population, until complete disappearance for sufficiently large dust density. For perpendicular ion temperature smaller than the parallel ion temperature the dustless Plasma features the proton fire-hose instability, which is also reduced by the prEsence of the dust population. The results obtained show that the fire-hose instability is more easily quenched by the prEsence of the dust than the proton cyclotron instability. For both instabilities, the prEsence of the dust affects the dispersion relation by the charge imbalance produced by the electron capture by the dust particles, and by the damping effect originated from the collisional charging of the dust particles.

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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.