equations. The manner in which these algorithms are used is explained

in section 5.3. Some of the algorithms are new, while some are adap-

tations of algorithms previously developed. Where existing algorithms

are used, the alterations to the problems necessary to allow their use

are detailed.


4.1 Decoupling

 Decoupling can result in significant simplification of the solu-

tion procedure for a set of indexed equations. Since the presence of

decoupling depends upon the function-variable and index output set

assignments made, it is desirable to choose these in such a way that

decoupling will result. In addition, the function ordering also

affects the degree to which decoupling is possible. Finally, the

direction in which the function indices are incremented (ascending or

descending), influences any decoupling. For a particular direction of

index incrementing, some IDM's may fully precedence order while others

may not. All IDM's for a function index must fully precedence order

for it to be a candidate for a decoupling index. Recall that decoupling

results in a full precedence ordering of function types. This is

equivalent to a full precedence ordering for an index, the index in this

case being function type. It has been shown that nesting a fully

precedence ordered index inside one which does not fully precedence

order results in increased function evaluations. This would be the

case if a decoupling index did not fully precedence order. What is

required, then, is an algorithm which will analyze the FVIM and IDM's

to choose the function ordering, function outputs, index outputs, and

direction of index incrementing in such a way as to decouple the