Constrained convergence

The convergence of PA(N)Q is investigated. The results are then used to obt ain information about the convergence of constrained Picard iteration Y-N = PXN, where XN+1 = AX(N) + B In particular, it is shown that, for given P, A and B there exists an initial condition X-0 = C for which Y-N converges, exactly when R[theta B] subset of or equal to R[theta(I-A)], where theta = [p(T), A(T), A(T)P(T),..., (A(m-1))P-T(T)](T) and m is the degree of the mi nimal polynomial of A.