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Floating Point Fault Tolerance with Backward Error Assertions
February 1995 (vol. 44 no. 2)
pp. 302-311

Abstract— This paper introduces an assertion scheme based on the backward error analysis for error detection in algorithms that solve dense systems of linear equations, A\mbi{x} = \mbi{b}. 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 O(n^2), compared to the O(n^3) complexity of algorithms solving A\mbi{x} = \mbi{b}. Unlike other proposed error detection methods, this assertion model does not require any encoding of the matrix A. Experimental results under various error models are presented to validate the effectiveness of this assertion scheme.

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Daniel Boley, Gene H. Golub, Samy Makar, Nirmal Saxena, Edward J. McCluskey, "Floating Point Fault Tolerance with Backward Error Assertions," IEEE Transactions on Computers, vol. 44, no. 2, pp. 302-311, Feb. 1995, doi:10.1109/12.364541
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