Breakdown-free version of ILU factorization for nonsymmetric positive definite matrices

In this paper a new ILU factorization preconditioner for solving large sparse linear systems by iterative methods is presented. The factorization which is based on AA-biorthogonalization process is well defined for a general positive definite matrix. Numerical experiments illustrating the performance of the preconditioner are presented. A comparison with the well known preconditioner RIFp of Benzi and Tůma is also included.