AN OPTIMIZATION PROBLEM ARISING FROM TEARING METHODS

Publisher Summary This chapter discusses an optimixation problem arising from tearing methods. It presents a graph theoretic interpretation of the problem, based on a bipartite graph. Because of the particular structure of A, a large, sparse, nonsingular, non-symmetric matrix, sometimes it is possible to save computation time and/or storage requirements implementing tearing methods. Tearing consists mainly of two parts: at first, the solution of the system A*x = b is computed, where A* has been obtained from A zeroing some elements; then, this solution are modified to take into account the real structure of the original system. This method may be necessary, even though not convenient, when it is not possible to process the original system Ax = b because of its dimension w.r.t. the dimension of the available computer. Further work is needed to determine how far it is the solution given by the heuristic algorithm from the optimum one. It is important to devise new heuristic procedures such that more flexibility is allowed introducing the possibility of limited backtracking. The parallelism between the nonsymmetric permutation problem and the symmetric permutation one suggests that some optimal reduction rules can be successfully implemented.