Ai. Zecevic et Dd. Siljak, BALANCED DECOMPOSITIONS OF SPARSE SYSTEMS FOR MULTILEVEL PARALLEL-PROCESSING, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 41(3), 1994, pp. 220-233
The objective of this paper is to present a recursive algorithm for pe
rmuting sparse matrices into the bordered block diagonal form. An outs
tanding feature of this algorithm is the resulting balance between the
border size and the size of the diagonal blocks, which gives rise to
an efficient multilevel scheme for parallel matrix factorization. This
scheme is characterized by good load balancing and low interprocessor
communications. In addition, it is specifically designed to minimize
fill in within the factored matrix in order to preserve the original s
parsity. Applications to power transmission systems are presented, tog
ether with a discussion of relevant parallelization and sparsity issue
s.