Scheduling affine parameterized recurrences by means of

The authors present new scheduling techniques for systems of affine recurrence equations. They show that it is possible to extend earlier results on affine scheduling to the case when each variable of the system is scheduled independently of the others by an affine timing-function. This new technique makes it possible to analyze systems of recurrence equations with variables in different index spaces, and multi-step systolic algorithms. This theory applies directly to many problems, such as dynamic programming, LU decomposition, and 2-D convolution, and it avoids in particular preliminary heuristic rewriting of the equations