Automatic Decomposition of Non-linear Equation Systems in Audio Effect Circuit Simulation
In the digital simulation of non-linear audio effect circuits, the arising non-linear equation system generally poses the main challenge for a computationally cheap implementation. As the computational complexity grows super-linearly with the number of equations, it is beneficial to decompose the equation system into several smaller systems, if possible. In this paper we therefore develop an approach to determine such a decomposition automatically. We limit ourselves to cases where an exact decomposition is possible, however, and do not consider approximate decompositions.