equations, with index limits defined by the blocking factors. For the

calculation of the Jacobian, estimated variable values are used. The

index ordering for the Jacobian has function type nested outermost,

as indicated in Fig. 4-4. For each function-variable partition in the

Jacobian [Fig. 4-4 a)], an output product is computed by multiplying the

elements corresponding to the index outputs for that function in that

variable. If a variable type is not a legal output for a function type,

the corresponding product is set to a very large positive number. These

products are then the weights used in the FVIM output set assignment,

as is shown in Fig. 4-4 b).

 While this procedure does not necessarily generate the true

maximum product output set assignment, it does generate the most nearly

maximum product output set assignment possible under the restrictions

for FVIM outputs.


4.4 Minimum Weighted Tearing

 Tear variables for a solution procedure with assigned output

variables are chosen using the minimum weighted tearing algorithm of

Pho and Lapidus (1973). If all variable weights are equal, the tearing

scheme chosen will be one with the minimum number of torn variable

types. The tear variables, however, are chosen by analysis of the FVIM.

The columns in the FVIM do not necessarily all represent the same

number of variables. The number of variables of a variable type is

determined by the function index definition (not the variable index

definitions, which may include decisions). The expected index ranges

can be used to calculate the expected number of variables for each

variable type. This number can then be used as the weight for the