A two levels algorithm for tearing

This paper deals with tearing methods for the solution of a large scale system of linear algebraic equations. A modification algorithm Is presented and evaluated with respect to other available techniques, namely, Householder\´s formula and Bennet\´s algorithm. Then, an optimization problem related to the "best" way of tearing a given matrix with a certain associated structure is stated and solved by proving it to be equivalent to the determination of a minimum essential set of a suitably defined hypergraph . A branch-and-bound algorithm for minimum essential set in , based on a number of local reduction rules is outlined. Finally, the application of the obtained results to the tearing problem is discussed and its complexity compared with decomposition method.