The Tailoring of Abstract Functional Specifications of Numerical Algorithms for Sparse Data Structures through Automated Program Derivation and Transformation

The automated application of program transformations is used to derive, from abstract functional specifications of numerical mathematical algorithms, highly efficient imperative implementations tailored for execution on sequential, vector and array processors. Emphasis is placed on transformations which tailor implementations to use special programming techniques optimized for sparse matrices. We demonstrate that derived implementations attain superior execution performance than manual implementations for two significant algorithms.

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