solving large sets of equations simultaneously, it is desirable to avoid

Newton-Raphson type solution procedures whenever possible. The alterna-

tive, tearing procedures, requires that certain variable values be

guessed or torn (these variables become the iterative variables to be

converged), all variable values are calculated algebraically including

the torn variables, and the new values of the torn variables are used

for the next iteration. The method continues until the criteria for

convergence are satisfied.

 A tearing solution procedure requires an output set assignment

for the algebraic solutions. An output set assignment is the assign-

ment to each equation of one of the variables occurring in that

equation is such a way that each variable is assigned to only one

equation. Not all variables need be assigned to equations; the

unassigned variables are "decision" variables. Early studies of the

nature of output set assignments were concerned with structural proper-

ties (Steward, 1962,1965). Later studies addressed the problem of

assigning an output set with the aim of enhancing the likelihood of

convergence (Edie, 1970) and developed effective algorithms for assign-

ing outputs when some criterion for optimality has been defined (Gupta,

1972; Gupta et al., 1974).

 An iterative solution procedure is made iterative by the presence

of tear variables which must be converged. iMany algorithms have been

developed for choosing tear variables in order to satisfy any of several

criteria, such as minimum number of torn variables or minimum sum of

weights of torn variables, where each variable is given a weight

(Sargent and Westerberg, 1964; Christensen and Rudd, 1969; Barkley and

Motard, 1972; Ramirez and Vestal, 1972; Pho and Lapidus, 1973).