Floating Point Fault Tolerance with Backward Error Assertions

This paper introduces an assertion scheme based on the brpwprd errw amlysis for error detection in algorithms that solve dense systems of linear equations, A z = 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 envjronment. The complexity of verifying assertions is O(n2) , compared to the O(n3) complexity of algorithms solving A z = 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.