Improving the performance of parallel triangularization of a sparse matrix using a reconfigurable multicomputer

Abstract

Many applications require the solution of a least-squares (LS) problem from a coefficient matrix and a measurement vector. In some cases, the solution must be obtained within a short period of time, requiring great computation power, as is the case of state estimation in electric power systems. In some cases, the coefficient matrix is a large and sparse one, requiring special techniques to reduce the computationtime and storage requirements. In these situations, fast Givens rotations are very well suited for parallel computers because they exhibit a great potential parallelism. In this paper we improve the performance of the fast Givens rotations algorithm for sparse matrices by means of using a reconfigurable multicomputer. A reconfigurable multicomputer is a message-passing multiprocessor in which the network topology can change during the execution of the algorithm. In this way, the interconnection network can match the communication requirements of a given algorithm. In this paper we show the improvement for applying this novel technique to improve the performance of the parallel fast Givens rotations, and we present general concepts related with it. This technique consists basically in placing the different processors in those positions in the network which, at each computational moment and according to the existing communication pattern among them, are more adequated for the development of such computation.