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What if we use almost-linear functions instead of linear ones as a first approximation in interval computations

In many practical situations, the only information that we have about measurement errors is the upper bound on their absolute values. In such situations, the only information that we have after the measurement about the actual (unknown) value of the corresponding quantity is that this value belongs to the corresponding interval: e.g., if the measurement result is 1.0, and the upper bound is 0.1, then this interval is [1.0−0.1, 1.0+0.1] = [0.9, 1.1]. An important practical question is what is the resulting interval uncertainty of indirect measurements, i.e., in other words, how interval uncertainty propagates through data processing. There exist feasible algorithms for solving this problem when data processing is linear, but for quadratic data processing techniques, the problem is, in general, NP-hard. This means that (unless P=NP) we cannot have a feasible algorithm that always computes the exact range, we can only find good approximations for the desired interval. In this paper, we propose two new metrologically motivated approaches (and algorithms) for computing such approximations.