On a modification of algebraic multilevel iteration method for finite element matrices

Today, multigrids and multilevel methods for solving a sparse linear system of equations are well known. They are both robust and efficient. In [6], the algebraic multilevel iteration (AMLI) method for finite element matrices has been proposed. However, this method has two restrictions on the properties of the original matrix, which can fail in practice. To avoid them and to improve the quality of the AMLI-preconditioner, a family of relaxation parameters is suggested and analyzed.