Bipartite Graphs and the Decomposition of Systems of Equations

Solving large systems of equations is a problem often encountered in engineering disciplines. However, as such systems grow, the effort required for finding a solution to them increases as well. In order to be able to cope with ever larger systems of equations, some form of decomposition is needed. By decomposing a large system into smaller subsystems, the total effort required for finding a solution may decrease. However, whether this is really the case of course depends on the additional effort required for obtaining the decomposition itself. In this thesis several aspects of the difficulty of obtaining such decompositions are explored.