Formal derivation of algorithms

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Abstract
In this paper we apply a formal approach for the derivation of dense linear algebra algorithms to the triangular Sylvester equation. The result is a large family of provably correct algorithms. By using a coding style that reflects the algorithms as they are naturally presented, the correctness of the algorithms carries through to the correctness of the implementations. Analytically motivated heuristics are used to subsequently choose members from the family that can be expected to yield high performance. Finally, we report performance on the Intel (R) Pentium (R) III processor that is competitive with that of recursive algorithms reported previously in the literature for this operation.

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