Fast structured sparse unary matrix operations on dense systolic arrays

The authors present a systematic method for increasing the efficiency of a class of systolic arrays implementing unary matrix operations. The proposed technique is primarily an analysis tool that has important applications in the design of computing structures with reduced computational complexity. The method uses the concept of a timing graph to display the evolution of computations as a function of the compute cycle. In an extension of previous results the concept of timing graph decoupling is introduced as a procedure to determine structured sparsity patterns that can be executed more efficiently in a dense array. The technique is applied to LU and QR decomposition arrays