Multivariate approximation theory: selection topics
Multivariate approximation theory: selection topics
VLSI array processors
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The systematic design of systolic arrays
Centre National de Recherche Scientifique on Automata networks in computer science: theory and applications
Nondifferentiable optimization
Optimization
Affine timings for systems of affine recurrence equations
PARLE '91 Proceedings on Parallel architectures and languages Europe : volume I: parallel architectures and algorithms: volume I: parallel architectures and algorithms
Time Optimal Linear Schedules for Algorithms with Uniform Dependencies
IEEE Transactions on Computers
Calculus of space-optimal mappings of systolic algorithms on processor arrays
Journal of VLSI Signal Processing Systems - Special issue: application specific array processors
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
The parallel execution of DO loops
Communications of the ACM
Loop Parallelization
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Constructive Methods for Scheduling Uniform Loop Nests
IEEE Transactions on Parallel and Distributed Systems
Systolic Array Synthesis by Static Analysis of Program Dependencies
Proceedings of the Parallel Architectures and Languages Europe, Volume I: Parallel Architectures PARLE
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Frequently, affine recurrence equations can be scheduled more efficiently by quadratic scheduling functions than by linear scheduling functions. In this paper, the problem of finding optimal quadratic schedules for affine recurrence equations is formulated as a convex nonsmooth programming problem. In particular, sufficient constraints for causality are used generalizing Lamport's condition. In this way, the presented problem formulation becomes independent of the problem size. The research tool AQUAD is described implementing this problem formulation. Several nontrivial examples demonstrate that AQUAD can be effectively used to calculate quadratic schedules for affine recurrence equations. Finally, it is shown how array processors can be synthesized from affine recurrence equations which are scheduled by quadratic functions with a singular Hessian matrix.