Computing a block incomplete LU preconditioner as the by-product of block left-looking A-biconjugation process

In this paper, we present a block version of incomplete LU preconditioner which is computed as the by-product of block A-biconjugation process. The pivot entries of this block preconditioner are one by one or two by two blocks. The L and U factors of this block preconditioner are computed separately. The block pivot selection of this preconditioner is inherited from one of the block versions of Gaussian elimination process. The main basis to propose such a block preconditioner is a connection between the Gaussian elimination process and the A-biconjugation algorithm. In the numerical experiment section, we have generated artificial linear systems. Then, we have computed the block and plain versions of this incomplete LU preconditioner. We have used these two preconditioners as the right preconditioner for linear systems. After that, the GMRES(50) method has been applied to solve the right preconditioned systems. The results indicate that the block preconditioner gives fewer number of iterations of GMRES(50) method than the plain version. Therefore, the block preconditioer has a better quality.