converge variables being assigned high weights. Another strategy for

assigning weights could be to assign low weights to variables in which

the functions are relatively insensitive, i.e., the output variable

will be insensitive to bad guesses in those variables.

5.3.5 Modified Jabobian and Convergence Matrices

 At this point a solution procedure has been developed. This alone

is not enough, for in order for a solution procedure to be useful it

must converge to the solution of the equations. To determine the

likelihood of convergence the subroutines "I4AMAT," "I5CMAT," and

"I6LMDA" are invoked. The first calculates the modified Jacobian

matrix, the "A-Matrix" which is discussed in the next chapter. On the

first pass through the program the A-Matrix actually is the Jacobian

matrix. The set of equations analyzed is the expanded set, with index

ranges defined by the blocking factors. Next the subroutine "I6CMAT"

is called to calculate the convergence matrix, or a.-Matrix, from the

A--Matrix. The a-Matrix gives an approximation (eact for linear

equations) of the growth of the error in the recycle variables from

iteration k to k+l. The expression for this s e e =; In order

for convergence to occur the eigenvalues of n must all be less than I in

magnitude. The subroutine "'I-ri.A" calculates the largest eignnv'alue of

a. This then can be used to determine the likelihood of convergence.

If the largest eigenvalue is less than 1 the solution procedure is

accepted.

5.3.6 ilodifications to Solution Procedur-es

 If a solution procedure is found to be non-convergent it must be

 modified in an attempt to improve its convergence characteristics. The

 subroutine "I7MPSP" is invoked to make modifications to the solution