期刊
JOURNAL OF COMPUTATIONAL SCIENCE
卷 14, 期 -, 页码 51-60出版社
ELSEVIER
DOI: 10.1016/j.jocs.2015.12.002
关键词
Algorithm-based fault tolerance; Resilient algorithms; Numerical methods
资金
- NSF [1058779, 0958311]
- U.S. Department of Energy Office of Science, Advanced Scientific Computing Research
- U.S. Department of Energy's National Nuclear Security Administration [DE-AC04-94AL85000]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [GRANTS:13889032] Funding Source: National Science Foundation
- Division Of Computer and Network Systems
- Direct For Computer & Info Scie & Enginr [0958311] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1058779] Funding Source: National Science Foundation
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. Furthermore, 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. (C) 2016 Elsevier B.V. All rights reserved.
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