A polynomial preconditioner for block tridiagonal matrices

This paper is concerned with the solution of block tridiagonal linear systems by the preconditioned conjugate gradient (PCG) method. If we consider a block AGE splitting of the coefficient matrix, it is possible to derive an additive polynomial preconditioner and to give conditions for such preconditioner to be symmetric positive definite.Numerical experiments on diffusion problem are carried out on CRAY Y-MP in order to evaluate the effectiveness of the parallel polynomial preconditioner