Sparsity-Oriented Ordering of Pivotal Operations on Network Equations

Abstract

For a considerably large network, the coefficient matrix of a system of network equations, such as a primitive Y- or Z-matrix, is generally very sparse. Thus, in the computer-aided analysis of such a system of equations, the exploitation of the sparsity of the matrix in terms of reductions inmemory space, processing time, and roundoff errors is of prime importance. Motivated by this problem, in the present paper we first define a sparsity-oriented pivotal operation and formulate an optimal ordering problem of these pivotal operations. Then we present an approach to the problem with the use of a newly defined “pivoting graph.”