and for j>i,
 i-i i-i
 a. = -[Aii +kiAikC.ki-, A.1 k+kiA-k kja,
 1 I ik ki L 1k kj

which proves 4), 5), and 6). The theorem is proved.

 Thus, it is always possible, for combinations of Gauss-Seidel

and Newton-Raphson, to evaluate the convergence matrix, a. This allows

an estimation of the convergence properties of a solution procedure

modified in this manner. Provided that the expanded incidence matrices

are kept reasonably small (through choice of blocking factors) the

problem of eigenvalue calculation does not become prohibitively time

consuming. It should also be noted that in general only one Gauss-

Seidel and one Newton-Raphson block will be present. Therefore, the

calculation of c from A remains reasonably simple.

 Presently, Gauss-Seidel and Newton-Raphson are the only different

solution procedures proposed and analyzed by GENIE. As alternative

solution procedures are implemented, means must be derived fioi

calculating the a matrix with them present.