FLOATING-POINT FAULT-TOLERANCE WITH BACKWARD ERROR ASSERTIONS

This paper introduces an assertion scheme based on the backward error analysis for error detection in algorithms that solve dense systems of linear equations, Ax = b. Unlike previous methods, this Backward Erro r Assertion Model is specifically designed to operate in an environmen t of floating point arithmetic subject to round-off errors, and it can be easily instrumented in a Watchdog processor environment. The compl exity of verifying assertions is O(n(2)), compared to the O(n(3)) comp lexity of algorithms solving Ax = b. Unlike other proposed error detec tion methods, this assertion model does not require any encoding of th e matrix A. Experimental results under various error models are presen ted to validate the effectiveness of this assertion scheme.