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Integrated System and Application Continuous Performance Monitoring and Analysis Capability

Brandt, James M.; Cook, Jeanine C.; Aaziz, Omar R.; Allan, Benjamin A.; Devine, Karen D.; Elliott, James J.; Gentile, Ann C.; Hammond, Simon D.; Kelley, Brian M.; Lopatina, Lena L.; Moore, Stan G.; Olivier, Stephen L.; Pedretti, Kevin P.; Poliakoff, David Z.; Pawlowski, Roger P.; Regier, Phillip A.; Schmitz, Mark E.; Schwaller, Benjamin S.; Surjadidjaja, Vanessa S.; Swan, Matthew S.; Tucker, Tom T.; Tucker, Nick T.; Vaughan, Courtenay T.; Walton, Sara P.

Abstract not provided.

A numerical soft fault model for iterative linear solvers

HPDC 2015 - Proceedings of the 24th International Symposium on High-Performance Parallel and Distributed Computing

Elliott, James J.; Hoemmen, Mark F.; Mueller, Frank

We present a fault model designed to bring out the \worst" in iterative solvers based on mathematical properties. Our model introduces substantially higher overhead, but smaller variance, than a fault model based on random bit ips. We also relate the statistics from our experiments back to the solvers' conffguration, and briey address the computational efiort that each model requires. Our approach requires signi ficantly fewer resources, while punishing our solvers with undetectable errors that require notable overhead for recovery. This work also illustrates the robustness of our resilient algorithms: Not only do we make forward progress in the presence of pathological faults, we always obtain the correct answer.

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Exploiting data representation for fault tolerance

Journal of Computational Science

Elliott, James J.; Hoemmen, Mark F.; Mueller, Frank M.

Incorrect computer hardware behavior may corrupt intermediate computations in numerical algorithms, possibly resulting in incorrect answers. Prior work models misbehaving hardware by randomly flipping bits in memory. We start by accepting this premise, and present an analytic model for the error introduced by a bit flip in an IEEE 754 floating-point number. We then relate this finding to the linear algebra concepts of normalization and matrix equilibration. In particular, we present a case study illustrating that normalizing both vector inputs of a dot product minimizes the probability of a single bit flip causing a large error in the dot product's result. Moreover, the absolute error is either less than one or very large, which allows detection of large errors. Then, we apply this to the GMRES iterative solver. We count all possible errors that can be introduced through faults in arithmetic in the computationally intensive orthogonalization phase of GMRES, and show that when the matrix is equilibrated, the absolute error is bounded above by one.

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16 Results
16 Results