An ILUCG algorithm which minimizes in the euclidean norm

This paper presents an algorithm which solves sparse systems of linear equations of the form Ax =y, where A is non-symmetric, by the Incomplete LU Decomposition-Conjugate Gradient (ILUCG) method. The algorithm minimizes the error in the Euclidean norm ‖xi − x‖2 , where xi is the solution vector after the ith iteration and x the exact solution vector. The results of a test on one real problem indicate that the algorithm is likely to be competitive with the best existing algorithms of its type.