In "Monte Carlo methods", chapter 7, Hammersley, the convergence condition for monte carlo to solve linear equations Ax=b is that the maximum absolute row sum norm of matrix H=A-I must be less than 1. Other material indicates that the condition is that spectral radius of matrix H should be less than 1. Other material says that matrix A should be diagonally dominant, These conditions are not equivalent as far as I can see; the spectral radius condition appears to be less strict than the other two. Could some one tell me which one is the true convergence condition?