On the derivation of parallel filter structures for adaptive eigenvalue and singular value decompositions

A graphical derivation is presented for a parallel filter structure (systolic array) for updating eigenvalue and singular value decompositions. The derivation of this array is non-trivial due to the presence of feedback loops and data contra-flow in the underlying signal flow graph (SFG). This would normally prohibit pipelined processing. However, it is shown that suitable delays may be introduced to the SFG by performing simple algorithmic transformations which compensate for the interference of crossing data flows and eliminate the critical feedback loops. The pipelined array is then obtained either by 2-slowing and retiming the SFG or by means of dependence graph scheduling and assignment, and turns out to be an improved version of the array presented in Moonen et al. (1993)