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.

中文翻译：

---

UaL 分解，MNA 矩阵 LU 分解的替代方法

本简介提供了一种替代众所周知的 LU 分解技术，主要用于改进的节点分析 (MNA) 电路解决方案。与传统的 LU 分解相比，这种称为上下分解的方法被证明在计算上是高效的，并且更不容易出现舍入错误。该方法是针对三种电路分析情况而开发的。首先，对于激励源都是电流源的情况，传统上是 MNA 表示的情况。在第二种和第三种情况下，我们允许在电路中输入电压源，使其成为混合源的最常见情况。结果表明，组合源表示可以将所有三种情况概括为一个类别。在准确性方面，由于该方法能够找到公因数（枢轴）并事先将其删除，因此所有带有余数的除法都被分类消除。这消除了可能的舍入误差，增加了技术的精度，特别是对于符号分析。