An analysis of algorithm-based fault tolerance techniques
Journal of Parallel and Distributed Computing
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Algorithm-Based Fault Detection for Signal Processing Applications
IEEE Transactions on Computers
Algorithm-Based Fault Tolerance on a Hypercube Multiprocessor
IEEE Transactions on Computers
The analysis and synthesis of efficient algorithm-based error detection schemes for hypercube multiprocessors
Algorithm-Based Error-Detection Schemes for Iterative Solution of Partial Differential Equations
IEEE Transactions on Computers
Extending Backward Error Assertions to Tolerance of Large Errors in Floating Point Computations
IEEE Transactions on Computers
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Abstract-Algorithm-based techniques are based on checking for the preservation of certain properties possessed by global data following a set of computations. This often involves the introduction of a check variable which is updated in such a manner that, in the absence of roundoff errors, it equals the value of some function which involves all the data elements participating in the algorithm. However, the fact that roundoff errors accumulate in different ways in the updates involving the check variables and the computations involving data elements make it highly unlikely that the equality is preserved exactly for an implementation of the algorithm on a real computer. Thus, the check step involves verifying the preservation of the equality to within a tolerance value. In this brief contribution, we propose a method for determination of the tolerance based on error analysis techniques. We present results on three numerical algorithms which show the effectiveness of our approach for data sets of varying sizes and data ranges.