A class of preconditioners based on matrix splitting for nonsymmetric linear systems

Given a general matrix splitting A=M-NA=M-N where M is nonsingular, a new factorization scheme in terms of factorized and splitting matrices is given using the Sherman–Morrison formula. Theoretical analysis shows that the factorization can give an LDU decomposition of A under some special choices. We propose and implement a class of preconditioners based on this factorization combining with dropping rules. A number of numerical experiments from discrete convection diffusion equation and some practical problems show that the new preconditioner is efficient, and is comparable to existing preconditioners in term of storage requirement and computational cost.