Partitioning of the System Equations

This section treats the partitioning of the system equations into the smallest irreducible subsystems, that is, the smallest groups of equations that must be solved simultaneously. Partitioning represents the first and easiest of the two phases of decomposition tearing (which is discussed in Section VI) is more difficult. 

As an illustration of partitioning consider the following equations written in functional form 

It can be seen by inspection that equations for functions f4 and /5 contain only variables x4 and x5, and that it is possible to solve these two equations for the values of x4 and x5 independently of the remaining equations. Also 

We first mention certain criteria for partitioning and tearing, and then describe methods of executing the partitioning. Tearing is treated in Section VI. 

Certain desirable features are sought in and certain limitations are imposed on any effective decomposition scheme. These are  

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