Matrix methods for the design and analysis of recurrent algorithms for multi-purpose systolic arrays

A matrix method for the design and analysis of systolic array algorithms is presented. The method starts by representing a nested loop algorithm as a set of matrices and an expression function. This representation is then mathematically integrated into the algorithm transformation technique of Moldavan (1982) and Fortes (1984). Using this framework, data position, distribution, velocity, and collision information can be computed along with processor element memory contents, all as functions of the systolic temporal vector. The systolic array synthesis equations are then derived. Their solution is a transformation matrix that generates a systolic algorithm with prespecified properties in terms of algorithm flow. Finally, the method is shown to be able to generate systolic algorithms for nonuniform recurrent algorithms such as the LU. Cholesky and QR decompositions