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<p>The authors provide an in-depth study of the various issues and tradeoffs available in algorithm-based error detection, as well as a general methodology for evaluating the schemes. They illustrate the approach on an extremely useful computation in the field of numerical linear algebra: QR factorization. They have implemented and investigated numerous ways of applying algorithm-based error detection using different system-level encoding strategies for QR factorization. Specifically, schemes based on the checksum and sum-of-squares (SOS) encoding techniques have been developed. The results of studies performed on a 16-processor Intel iPSC-2/D4/MX hypercube multiprocessor are reported. It is shown that, in general, the SOS approach gives much better coverage (85-100%) for QR factorization while maintaining low overheads (below 10%).</p>
hypercube multiprocessors; algorithm-based error detection; numerical linear algebra; QR factorization; encoding; checksum; sum-of-squares; 16-processor Intel iPSC-2/D4/MX; encoding; error detection; linear algebra; multiprocessing systems; software engineering.

P. Banerjee and V. Balasubramanian, "Tradeoffs in the Design of Efficient Algorithm-Based Error Detection Schemes for Hypercube Multiprocessors," in IEEE Transactions on Software Engineering, vol. 16, no. , pp. 183-196, 1990.
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