A block version algorithm to approximate inverse factors

An approach to compute sparse approximate inverse factors of matrix A is based on a bordering technique. In this method in each step one row and column of inverse factors are computed. In this paper, we show that, in each step, how we can obtain m rows and m columns of inverse factors of A. This method is appealing for parallel computers. Also we show that how this method can be implemented for linear systems that arises from a domain decomposition method for partial differential equations. Numerical experiments show that the new approach reduces computational cost of constructing the preconditioner and the new preconditioner retains the efficiency and robustness of the primitive version.