A convergence improvement of the BSAIC preconditioner by deflation

Abstract We have proposed a block sparse approximate inverse with cutoff (BSAIC) preconditioner for relatively dense matrices. The BSAIC preconditioner is effective for semi-sparse matrices which have relatively large number of nonzero elements. This method reduces the computational cost for generating the preconditioning matrix, and overcomes the performance bottlenecks of SAI using the blocked version of Frobenius norm minimization and the drop-threshold schemes (cutoff) for semi-sparse matrices. However, a larger parameter of cutoff leads to a less effective preconditioning matrix with a large number of iterations. We analyze this convergence deterioration in terms of eigenvalues, and describe a deflation-type method which improves the convergence.