A new version of the arithmetic mean method for solving block tridiagonal linear systems

In this report we consider a new version of the arithmetic mean method for solving large block tridiagonal linear systems. The iterative method converges for systems with symmetric positive definite or positive real matrices or irreducible L-matrices with a strong diagonal dominance. When the coefficient matrix is symmetric positive definite, an additive preconditioner for the conjugate gradient method is derived.The Fortran 77 code carried out on multivector computer Cray Y-MP implementing the algorithm above, are reported in appendix