… In Section 2, we briefly review interval and affine arithmetic and its extension to complex
arithmetic. In Section 3, we propose an adaptive discretization method for condition (8) and …

… In parallel to interval arithmetic (IA), many contributions were addressed for affine arithmetic
since more general sets than boxes can be defined. In this context, the parallelotopes …

… We provide also an approach based on affine arithmetic [14], in the same spirit than [23],
in order to increase the width of initial values while keeping low complexity on arithmetic …

… In order to represent sets of reals, we use affine arithmetic [9]: it is a refinement over interval
arithmetic [18] which is able to keep track of linear correlations between variables. A set of …

… , based on the use of affine arithmetic. This alternative technique has been developed to
improve the self-validated numerical analysis. Within affine arithmetic, the quantities of interest …

… For completeness of presentation, we first review interval and affine arithmetic which are …
that can be a more precise substitute for interval or affine arithmetic. Finally, we continue with a …

… The authors in [11] proposed a method based on iterative sweep load flow and affine arithmetic
… For example, [28] proposed to use interval and affine arithmetic, power flow computation …

… To study them as a model of real-valued computation, we introduce the concept of Max-Affine
Arithmetic Programs and show equivalence between them and NNs concerning natural …

… It is essential to develop the affine arithmetic to improve the … For instance, an affine
arithmetic-based forward-backward … method based on affine arithmetic considering uncertainties …

… Following the philosophy of the affine arithmetic, within the framework of structural analysis,
the so-called improved interval analysis via extra unitary interval has been proposed [30], [33…