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 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 0(n2), compared to the 0(n3) complexity of algorithms solving Ax = 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.
Bibliographical noteFunding Information:
Manuscript received November 29, 1993; revised April 21, 1994. This work was supported in part by the Hewlett-Packard Resident Fellowship, by the National Science Foundation under Grants MIP-8709128, CCR-8821078, and CCR-8813493, by the Army Research Office under Grant DAAL03-87-K-0095, and by the Innovative Science and Technology Office of the Strategic Defense Initiative Organization administered through the Office of Naval Research under Contract “14-85-K-0600. The work of G. H. Golub was supported in part by the National Science Foundation under Grant NSF CCR-8821078. The work of E. J. McCluskey was supported in part by the Innovative Science and Technology Office of the Strategic Defense Initiative and administered through the Office of Naval Research under Contract N0001492-J-1782, and in part by the National Science Foundation under Grant MIP-9107760. The work of D. Boley was carried out while on leave at the Stanford University Computer Science Dept., whose hospitality is gratefully acknowledged.
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