Theory of an interval algebra and its application to numerical analysis

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Verification methods: rigorous results using floating-point arithmetic (2010, background): “One reason is that L is generally well-conditioned, even for ill-conditioned A, despite the fact that Viswanath and Trefethen (1998) showed that random lower triangular matrices are generally ill-conditioned.”
On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models (2018, methodology): “In this paper, we study interval bound propagation (IBP), which is derived from interval arithmetic [14, 15, 28]: an incomplete method for training verifiably robust classifiers.”