… To avoid some limitations with interval arithmetic, other kinds of arithmetic may bu used such
as affine arithmetic [3]. Both arithmetic are available in IBEX. Consider some function g : Rn …

… , extracting shape form shading, surface height recovery, reverse engineering, box-splines,
the Plateau Problem, splines (a variety of papers), transfinite blending, and affine arithmetic. …

… a higher-order inclusion rule set such as affine arithmetic [3] or midpoint-Taylor arithmetic [7].
… Interval methods for raycasting implicit surfaces with affine arithmetic. In Proceedings of XII …

… )-based proof engine with an affine arithmetic (AA)-based engine that can more accurately
… Affine arithmetic (AA) [9] is a refinement to IA that addresses the above problem by keeping …

… Affine arithmetic represents a range of possible values by an … Probabilistic Affine Arithmetic
The worst-case error can be … probability distributions is probabilistic affine arithmetic [4]. Here, …

… We evaluate it in interval rather than affine arithmetic for simplicity: \([\varvec{F}](\varvec{x})=
1 + [0,\frac{1}{3}] \left( 1+[\frac{1}{3},1] [-1,-\frac{2}{3}]\right) ^2 \varvec{x}= 1 + [0,\frac{7^2}{3^5…

… In this section, we first briefly present our encoding of sets using affine arithmetic (Section
3.1) and show how explicit Runge-Kutta like numerical integration methods (Section 3.2) and …

… mance of affine arithmetic as a replacement of interval arithmetic in interval methods for ray
tracing implicit surfaces. In this work we analyze and evaluate the algorithms developed by …

Metaheuristic optimization methods, as model-free approaches, are expected to be applicable
to practical issues (eg, engineering problems). Although optimization methods have been …

… throughout the system thanks to an affine arithmetic based simulation. The values of …
Nevertheless, in the case of recursive systems, several iterations for the affine arithmetic based …