The LU factorization method is one of the most important methods in numerical applications, used for solving square systems of linear equations. This method enables the decomposition of the system matrix into the product of two triangular matrices, which enables a faster solution for the system. The importance of the LU factorization method becomes especially evident in the analysis of complex networks, such as electrical circuit networks. In this context, LU factorization plays a key role in the optimization and analysis of voltages, currents, and other parameters under both static and dynamic conditions. Through this process, it is possible to save time and computational resources when solving networks that involve a large number of equations, as well as to analyze the behavior of the network under different load conditions. This paper explores the application of LU factorization in the analysis and optimization of electrical circuit networks because once the system matrix is factorized, similar systems can be solved quickly without the need to factorize the matrix again. In our case, this means that when changes occur in the network (such as variations in load, the addition of new components, or changes in the parameters of existing ones), LU factorization enables rapid resolution of new systems of linear equations without the need for re-modeling the entire system.