Showing papers by "Alberto Sangiovanni-Vincentelli published in 1976"

A two levels algorithm for tearing

Abstract: 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 A 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 H . A branch-and-bound algorithm for minimum essential set in H , 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 LU decomposition method.

A note on bipartite graphs and pivot selection in sparse matrices

Abstract: In this note a bipartite graph representation is proposed for the study of pivot strategies on sparse matrices Using this representation, an algorithm which fullfills the Brayton's condition for Gaussian elimination optimality has been devised

An optimization problem arising from tearing methods

Abstract: 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.