On the synthesis of multi-linear arrays with flexible compute time

The paper overviews a systematic method to design and analyze flexible multi-linear systolic arrays. The arrays have time-optimal performance for general dense matrices and can be modified to use efficiently certain sparsity patterns. The method reported can be divided into two major parts. The first is a general design method to create a regular graph representation of algorithms. The resulting graph can be mapped onto time-optimal multi-linear arrays to implement the generic form of the algorithm. The second part develops procedures to analyze and modify the graph representation of the algorithm. The analysis is used to detect sparsity patterns that can be used to reduce the overall execution time for specific algorithm realizations