In the paper, GMRES is applied to various large matrices appearing in the 3D field analyses. By changing the condition of the matrices, effective pre-conditioning of the matrix is to be searched for. Also studied is a relationship between the residual norm and the precision evaluated during GMRES. The paper clarified the residual norm, which is indirectly computed in GMRES and has so far been used as a measure of precision, cannot be used as an indicator of solution's accuracy. After reasoning a deterioration of the precision, GMRES (ml), which solves matrix with a modified iterative scheme, is proposed. It is to be confirmed that GMRES(ml) is faster and more accurate than any of GMRES and its modified version, GMRES (m).