egligible contribution. Technically, this implies that we remove all paths for which Hm(s) H(s) We refer to appendix A for more details on HTM norms. This simplification requires of course numerical data, or other prior knowledge on the sys- tem, to be available. 4.3.4 Data structures In storing the HTM, it is not needed to store every matrix element separately. From the structural relation (3.53) derived in section 3.3.4, it is seen that it is sufficient to only store the nonzero elements H o(s) of the HTM's 0-th column. When these elements are known over the entire frequency range w E [-00,00], one is able to compute all other elements of the HTM. SymbolicHTM, therefore, stores HTMs by means of expressions 4.3 AUTOMATED SYMBOLICLPTV SYSTEM ANALYSIS for the elements of their 0-th column. As a note aside, we mention that this particular choice in storing HTMs best suits the power series expansion method that SymbolicHTM is using to perform HTM inver- sions. Algorithms performing the inversions, for example using rank-reduced approxi- mations, may require alternate ways for storing HTMs and their elements. 4.3.5 Computational flow of the SymbolicHTM algorithm Fig. 4.22 shows the global outline of the computational flow of the Symbolic HTM algorithm. It starts from a system block diagram model and consists of three steps. In a first (preprocessing) step, the input model's feedback loops are cut by introducing a set of loop variables. During the second step, which comprises the actual symbolic com- putations, these loop variables are eliminated using symbolic Gaussian elimination in order to obtain expressions for the input-output HTM elements. In a final (postprocess- ing) step, these expressions can be simplified to obtain more compact and better read- able expressions. The latter is only possible if numerical data are available to control the truncation error [Gie91, Gie94]. In what follows, we explain each of these steps in more detail. 4.3.5.1 Breaking the loops In a first step, all loops in the block diagram a