Complexity of matrix product on modular linear systolic arrays for algorithms with affine schedules

This paper investigates the computation of matrix product on both partially pipelined and fully pipelined modular linear arrays. These investigations are guided by a constructive and unified approach for both target architectures. First, permissible affine input functions are identified by a set of necessary and sufficient conditions for various conflict avoidance. This first study also leads to complexity results. Then, algorithms whose performance represents an improvement over the best previously known bounds are exhibited.