References in raw/Page_27.html

• Automatic accuracy-guaranteed bit-width optimization for fixed and floating-point systems
  WG Osborne, RCC Cheung... - ... Conference on Field ..., 2007 - ieeexplore.ieee.org
  ... 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. ...
  

• A generic scheme for combining multiple inclusion representations in numerical constraint propagation
  XH Vu, D Sam-Haroud, BV Faltings - 2004 - infoscience.epfl.ch
  ... 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 ...
  

• A mixed interval power flow analysis under rectangular and polar coordinate system
  C Zhang, H Chen, H Ngan, P Yang... - IEEE Transactions on ..., 2016 - ieeexplore.ieee.org
  ... 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, ...
  

• On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic
  B G-Tóth, LG Casado, EMT Hendrix... - Journal of Global ..., 2021 - Springer
  ... This paper introduces several linear relaxations using gradient information and Affine
  

• Affine Iterations and Wrapping Effect: Various Approaches
  N Revol - arXiv preprint arXiv:2201.00513, 2022 - arxiv.org
  ... 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 ...
  

• Verified reachability analysis of continuous systems
  F Immler - International Conference on Tools and Algorithms for ..., 2015 - Springer
  ... 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/...
  

• Interval power flow calculation algorithm for multi-terminal dc distribution networks considering distributed generation output uncertainties
  Q Liu, S Wang, Q Zhao, K Wang - ... Generation, Transmission & ..., 2021 - Wiley Online Library
  ... 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 ...
  

• Affine-Contractor Approach to Handle Nonlinear Dynamical Problems in Uncertain Environment
  NR Mahato, S Rout... - Mathematical Methods in ..., 2020 - Wiley Online Library
  ... 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 ...
  

• AFFINE ANALYSIS FOR UNCERTAINTY OF GAS LOAD IN INTEGRATED ELECTRICAL AND NATURAL-GAS SYSTEM
  S Yuan, S Wang, K Wang - 2019 - energy-proceedings.org
  ... 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 ...
  

• Automatically Generated Nonlinear Analog Circuit Models Enclosing Variations with Intervals and Affine Forms for Reachability Analysis
  M Rechmal-Lesse, GA Koroa... - ... on Design and ..., 2020 - ieeexplore.ieee.org
  ... 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 ...