A new class of general-base matrices and a formalism for optimal parallel/pipelined computer architecture

A new class of general-base matrices and a novel matrix formalism which provides mathematical tools for the search for and the attainment of optimal parallel/pipelined computer architecture are presented. “Sampling matrices”, “span matrices” and “p^k-optimal” matrices are shown to bridge the gap between algorithmic description and computer architecture. Optimal memory partitioning, addressing elimination and a minimization of shuffle operations are obtained using the proposed formalism. The approach is illustrated using algorithms of generalized spectral analysis which are more complex and general than the usually factored Fourier transform. New general-base factorizations for three different forms of the Chrestenson transform are obtained. A class of optimal parallel and parallel-pipelined general-base processors for the implementation of the Chrestenson transform are presented