Abstract
In the tableau approach to large‐electrical‐network analysis, as well as in structure analysis, the finite‐element method, linear programming etc., a very sparse linear algebraic set of equations Ax = b has to be solved repeatedly. To efficiently solve the system via Gaussian elimination, an optimization problem has to be faced: the selection of a pivot strategy to maintain the sparsity of the matrix A. It is possible also to follow a different strategy to fully exploit the sparsity of A, i.e. to transform A into an equivalent but more convenient form. Both of these problems have been studied and partially solved by means of directed graphs associated with A when symmetric permutations on A are allowed.
In this paper, a graph theoretical interpretation has been given to nonsymmetric permutations on A, which can be considered a fundamental step towards the solution of the above‐mentioned optimization problems. This interpretation is obtained through decomposition theorems on nonsymmetric permutations, correspondence theorems between column (row) permutations and topological operations on a directed graph representing A.