A new always cancellation-free approach to the multilevel symbolic analysis for very large electric networks

The paper presents an algorithm of the exact symbolic network function analysis that deals with circuits with any size. The only condition is to decompose the whole circuit into smaller sub-circuits. The decomposition is the multi-level hierarchical one. What is more, the calculation for each level can be done only once and the partial results can be reused any time. A higher level subcircuit does not need too much information about a lower one. The method can be easily implemented in multiprocessor or distributed systems. Although multilevel and compressed structure, symbolical value remains cancellation-free and any path from the root to the terminal vertex represent a single term. Thus, a large-scale and small-scale sensitivities calculation and elimination of less significant terms become simply and natural. To get the s-Expanded form, the fast algorithm based on sparse polynomial multiplication methods can be applied.