References in raw/Page_60.html

• An interval compiler for sound floating-point computations
  J Rivera, F Franchetti, M Püschel - 2021 IEEE/ACM ..., 2021 - ieeexplore.ieee.org
  ... affine arithmetic is roughly the same and double-double outperforms both. We conclude that
  

• Bitwidth customization in image processing pipelines using interval analysis and SMT solvers
  S Purini, V Benara, Z Choudhury... - Proceedings of the 29th ..., 2020 - dl.acm.org
  ... extent using affine arithmetic analysis. A detailed discussion on affine arithmetic analysis is ... In this section, we show how interval and affine arithmetic based range analysis techniques ...
  

• Enabling practical uses of arithmetic transform: a comprehensive analysis
  Z Zilic, K Radecka - Proceedings of 9th international workshop on ..., 2009 - iml.ece.mcgill.ca
  ... [12] develop a tool for Matlab specifications, while [5] use static affine arithmetic (AA) modeling, but only for the wordlength determination, similar as Pu and Ha [17]. Affine arithmetic ...
  

• Daisy-framework for analysis and optimization of numerical programs (tool paper)
  E Darulova, A Izycheva, F Nasir, F Ritter... - ... Conference on Tools ..., 2018 - Springer
  ... Daisy extends this support by implementing these operations in interval and affine
  

• Microgrids energy management systems: A critical review on methods, solutions, and prospects
  MF Zia, E Elbouchikhi, M Benbouzid - Applied energy, 2018 - Elsevier
  ... The proposed approach is solved by affine arithmetic and stochastic weight tradeoff PSO-based ... Scenario generation and reduction method, point estimate method, and affine arithmetic ...
  

• アフィン演算を用いた常微分方程式の初期値問題の精度保証付き解法
  宮田孝富， 柏木雅英 - 電子情報通信学会技術研究報告. NLP, 非線形問題, 2003 - ci.nii.ac.jp
  ... 精度保証付き解法 Long Time Integration for IVPs of ODEs Using Affine Arithmetic ... On the other hand, we are also concerned with Affine Arithmetic (AA). AA is a hopeful ... Affine Arithmetic ...
  

• Robustness measurement of integrated circuits and its adaptation to aging effects
  M Barke, M Kaergel, M Olbrich... - Microelectronics ..., 2014 - Elsevier
  ... digital circuits on gate level and their robustness against degradation due to aging effects like NBTI or HCI and the analysis of analog/mixed-signal circuits using affine arithmetic for ...
  

• Introduction to the Special Issue on Computer Arithmetic
  J Hormigo, JM Muller, S Oberman... - IEEE Transactions ..., 2017 - ieeexplore.ieee.org
  ... encompass interval arithmetic, algorithms and applications and related topics such as the use of floating-point arithmetic for implementation issues, variants such as affine arithmetic or ...
  

• RINO: Robust INner and Outer Approximated Reachability of Neural Networks Controlled Systems
  E Goubault, S Putot - International Conference on Computer Aided ..., 2022 - Springer
  ... of automatic differentiation and numerical evaluation by affine arithmetic, as described in eg [9]... a simple propagation of affine forms by affine arithmetic in the network: linear transformers ...
  

• Dynamic Modeling of Differential Bevel Gear with Uncertain-but-Bounded Parameters
  M Haddar - Advances in Materials, Mechanics and Manufacturing ..., 2021 - books.google.com
  ... the uncertain parameter x, and ˆe1 is the affine arithmetic variable. Where: Δx stands for the ... Where: sI t and uIt denote as the affine arithmetic variables. The displacement vector can be ...