CHAPTER 3

 SOLUTION PROCEDURES FOR INDEXED EQUATION SETS



 The last chapter detailed some restrictions which are placed on

the solution procedure developed. Other restrictions, along with their

motivations, will be presented in this chapter. In order that efficient

algorithms be written which can derive a solution procedure for indexed

equations, it is desirable that theorems be developed which can be used

to eliminate many of the possible choices open to the algorithms. This

chapter presents many such useful theorems, along with comments on their

application to problems. Most of the properties are related to a

single example problem presented in the beginning of the chapter.


3.1 Definitions

 Before proceeding with the example it is helpful to define some

of the terms used throughout the chapter.

3.1.1 FVIM Outputs

 As discussed in the last chapter, the FVIM must be output set

assigned. The variable types chosen as outputs are called the "FVIM

outputs."

3.1.2 FVIM Decisions

 In general, the number of variable types in an FVIM will be

 greater than the number of function types. When this is the case, some

 of the variable types cannot be assigned as outputs. These variable