Solution of large sparse systems by ordered triangular factorization

Analysis and/or control problems arising in utility systems are often of high dimensionality. As a result, the usual symbology of formal vector-matrix notation can obscure structural properties of the system or model which might otherwise allow very simple numerical solution. Simultaneous sparse systems arising from a number of different areas are shown to be of this type, including problems of electric power flow, water distribution, mechanical structure analysis, differential equation solution, optimal control, and linear programming. All are highly amenable to efficient solution schemes employing the sparse-matrix method of ordered triangular factorization.