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<p><it>Abstract—</it> This paper introduces an assertion scheme based on the <it>backward error analysis</it> for error detection in algorithms that solve dense systems of linear equations, <math><tmath>A\mbi{x} = \mbi{b}</tmath></math>. Unlike previous methods, this Backward Error Assertion Model is specifically designed to operate in an environment of floating point arithmetic subject to round-off errors, and it can be easily instrumented in a Watchdog processor environment. The complexity of verifying assertions is <math><tmath>O(n^2)</tmath></math>, compared to the <math><tmath>O(n^3)</tmath></math> complexity of algorithms solving <math><tmath>A\mbi{x} = \mbi{b}</tmath></math>. Unlike other proposed error detection methods, this assertion model does not require any encoding of the matrix <math><tmath>A</tmath></math>. Experimental results under various error models are presented to validate the effectiveness of this assertion scheme.</p>

E. J. McCluskey, N. Saxena, S. Makar, G. H. Golub and D. Boley, "Floating Point Fault Tolerance with Backward Error Assertions," in IEEE Transactions on Computers, vol. 44, no. , pp. 302-311, 1995.
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