ASPEN OneLiner employs the classical sparse matrix methods as well as the recently-developed sparse vector methods.
Sparse matrix methods are well-known in the utility industry. The classical reference is:
W.F. Tinney and J.W. Walker, "Direct Solutions of Sparse Network Equations by Optimally ordered Triangular Factorization," Proceedings of the IEEE, pp. 1801-09, November 1967.
Sparse vector methods were discovered only a few years ago, and they are much less well known. The original paper on the sparse vector method is the following:
W.F. Tinney, V. Brandwajn and S.M. Chan, "Sparse Vector Methods," IEEE Trans. on Power Apparatus and Systems, pp. 295-301, February 1985.
The sparse vector methods exploit, in addition to the high percentage of zeroes in the matrix, the extremely sparse vectors in fault calculations.
These advanced solution techniques are the key to the program's efficiency and modest storage requirements.