Affine Arithmetic: Concepts and Applications

By L. Figueiredo, Jorge Stolfi. 2004

357 citations recorded by the source corpus.

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Formal Security Analysis of Neural Networks using Symbolic Intervals (2018, background): “A key challenge in ReluVal is the inherent overestimation caused by the input dependencies [8, 39] when interval arithmetic is applied to complex functions.”
An Introduction to Affine Arithmetic (2003, background): “Affine arithmetic(AA) is one of several SVC models that were proposed to overcome the error explosion problem of standard IA [5, 10, 8 ]. Besides recording a range for each ideal quantity, affine arithmetic also keeps track ofcorrelations between those quantities.”
A Range Arithmetic-Based Optimization Model for Power Flow Analysis Under Interval Uncertainty (2013, methodology): “A good approximation function that is reasonably accurate and not very expensive to compute can be identified by applying the Chebyshev’s approximation theory for univariate functions [16], which furnishes an algorithm for finding the optimum coefficients of the affine approximation function.”
Verification methods: rigorous results using floating-point arithmetic (2010, methodology): “made substantial use of proof techniques based on floating-point arithmetic (for other examples see Frommer (2001)).”
An Affine Arithmetic-Based Methodology for Reliable Power Flow Analysis in the Presence of Data Uncertainty (2010, background): “These drawbacks make the application of IA to power flow analysis complex and time consuming.”