UaL Decomposition, an Alternative to the LU Factorization of MNA Matrices

Abstract

This brief presents an alternative to the well know LU factorization technique dominantly used in modified nodal analysis (MNA) circuit solutions. The method, called upper and lower decomposition, is proven to be computationally efficient as well as less prone to round off errors compared to the traditional LU factorization. The method is developed for three cases of circuit analysis. First, for situations where the excitation sources are all current sources, as traditionally is the case for MNA representation. In the second and third cases we allow input voltage sources in the circuit, making it the most general case of mixed sources. It is shown that a combined sources representation can generalize all three cases into one category. In terms of accuracy, because of the capability of the method to find the common factors (pivots) and remove them before hand, all divisions with remainders are categorically eliminated. This removes possible round off errors, adding to the precision of the technique, particularly for symbolic analysis.