New ordering methods for sparse matrix inversion via diagonalization

Two new ordering methods that can be used to reduce the elements in the inverse factors of a sparse matrix are proposed. Compared with all other commonly used ordering methods, the new methods will produce less fill-in elements. The proposed methods are based on the diagonalization of A via the use of a transformation matrix, C. A new node sequence for the power network and all the elements of the C matrix are generated in only a single stage instead of the conventional LDU decomposition followed by a series of multiplications for W-matrix. The methods may be used for the parallel solution of sparse matrix equations. Test results show that the proposed methods can reduce the computation burden effectively.