Railway computation for infinite linear systems

The problem of solving an infinite system of linear equations finitely expressed is addressed. Modifications of the Gauss-Seidel method are presented, especially suitable for the implementation on SMP machines with a small number of processors. One of the proposed parallel algorithms, which concentrates the computational efforts where they are most neeeded, results to be more efficient than the sequential algorithm, even from the point of view of the total number of operations.