An ILU preconditioner for nonsymmetric positive definite matrices by using the conjugate Gram–Schmidt process

The present paper investigates the approach mentioned, but not developed, in [Benzi, Tuma, Numer. Linear Algebra Appl. 10 (2003)]. In this approach, using a conjugate Gram–Schmidt algorithm, an ILU preconditioner whose existence is guaranteed for any nonsingular (symmetric and nonsymmetric) real positive definite matrix is obtained. Numerical results on some nonsymmetric positive definite matrices demonstrate the efficiency of the method.