… affine arithmetic are designed to optimize. The range analysis stage in our system combines
interval and affine arithmetic … interval arithmetic, whereas it does if you use affine arithmetic. …

… In order to illustrate the flexibility and efficiency of the proposed scheme, in Section 4 we
propose improvements on affine arithmetic and then devise from the scheme several new …

… It is based on affine arithmetic which is a self-validated numerical analysis and serves to
improve the interval results through optimization method. Since no approximation is presumed, …

… This paper introduces several linear relaxations using gradient information and Affine
Arithmetic and experimentally studies their efficiency compared to traditional lower bounds …

… The other technique is the use of affine arithmetic, as advocated by Rump in a private
communication. In the experimental results presented below, each technique is associated to a …

… We build on our formalization of affine arithmetic and the Euler method [15]. The verification
is carried out with respect to the theory of ODEs in the interactive theorem prover Isabelle/…

… algorithm and affine arithmetic, an interval PFC algorithm is presented to handle the
uncertainties of distributed generation output powers and loads. The affine arithmetic based interval …

… interval dependency problem, affine arithmetic, and its applications. … [19] handled interval-type
and affine arithmetic-type … Next, we consider an example to show that how affine arithmetic …

… This paper proposes an affine arithmetic-based method to analyze the influence by fluctuation
of gas load for IENGS which is composed of distribution network and low-pressure gas …

… This paper is structured as follows: First we describe the necessary background on
reachability analysis, interval arithmetic and affine arithmetic in Sec. II. Then we present the …