A parallel preconditioner for block tridiagonal matrices

In this report we consider two parallel additive preconditioners for solving block tridiagonal linear algebraic systems by the preconditioned conjugate gradient (PCG) method. If we consider two different splittings of the coefficient matrix, the first suggested by Evans and others and the second by authors of this report, it is possible to derive two parallel additive polynomial preconditioners of order m and to give conditions for such preconditioners to be symmetric positive definite. A Fortran implementation of the PCG method on Cray Y-MP has been developed in order to evaluate the effectiveness of the considered polynomial preconditioners. The numerical results carried out with this program permit to analyse the two preconditioners with respect to the complexity and the accuracy.The Fortran 77 codes carried out on multivector computer Cray Y-MP implementing the algorithms above, are reported in appendix.