ILU Pretreatment Householder-GMRES (m) Algorithm ⋆

Combining with preconditioning technologies and Householder transform, we apply a splitting pretreatment to the GMRES (m) algorithm and propose a kind of Incomplete LU decomposition pretreatment HGMRES (m) algorithm. Compared with the Arnoldi-GMRES (m) algorithm, the presented algorithm can improve the accuracy and efficiency of the solution. Numerical examples prove that the new algorithm is numerically stable and has higher computational precision and efficiency than the Arnoldi-GMRES (m) algorithm.