ON A BPX- PRECONDITIONER FOR LARGE SCALES

There are some different types of BPX multilevel precoditioners that are used for elliptic problems. In the most effective type, we need to compute the largest eigenvalues of the stiffness matrices in each level where is resulted from discretization of a variational boundary value problem. However, in the large scales, determining the eigenvalues of the stiffness matrix in the finest level is not generally easy except for some especial matrices . In this paper, we present a kind of BPX multilevel preconditioner which is suitable for symmetric positive definite system. In fact, with a change in the BPX preconditioner, we find a new preconditioner which is suitable for large scales.