References in raw/Page_58.html

• Interval power flow analysis using linear relaxation and optimality-based bounds tightening (OBBT) methods
  T Ding, R Bo, F Li, Q Guo, H Sun... - IEEE Transactions on ..., 2014 - ieeexplore.ieee.org
  ... Furthermore, in comparison to Affine Arithmetic method [15], we can see that the proposed method produces lower bounds and upper bounds that are significantly closer to the true ...
  

• Fast interval branch-and-bound methods for unconstrained global optimization with a ne arithmetic
  LH de Figueiredoy, R Van Iwaardenz, J Stolx - 1997 - ic.unicamp.br
  We show that faster solutions to unconstrained global optimization problems can be obtained by combining previous accelerations techniques for interval branch-andbound methods ...
  

• Determining uncertainty bounds for eigenvalues
  MI Friswell, U Prells, JET Penny - Proceeding of ISMA, 2004 - researchgate.net
  ... discussion and examples that specifying the parameter uncertainty using interval analysis can lead to very complex sets of eigenvalues, and specifying these through affine arithmetic or ...
  

• A Digital Twin with Runtime-Verification for Industrial Development-Operation Integration
  SDC Saratha, C Grimm... - 2021 IEEE International ..., 2021 - ieeexplore.ieee.org
  ... The Java Library jAADD creates the reachability models which constitutes the data structures of Affine Arithmetic Decision Diagrams (AADD, [14]). Such objects can be naturally stored ...
  

• A logical product approach to zonotope intersection
  K Ghorbal, E Goubault, S Putot - International Conference on Computer ..., 2010 - Springer
  ... 2.1 Affine Arithmetic and Zonotopes Affine arithmetic is an extension of interval arithmetic on affine forms, first introduced in [4], that takes into account affine correlations between ...
  

• Towards an industrial use of FLUCTUAT on safety-critical avionics software
  D Delmas, E Goubault, S Putot, J Souyris... - ... Workshop on Formal ..., 2009 - Springer
  ... in real numbers based on generalized affine arithmetic. In: Riis Nielson, H., Filé, G. (eds.) ... Perturbed affine arithmetic for invariant computation in numerical program analysis. CoRR, abs/...
  

• アフィン演算の実装方法について
  宮前知隆， 柏木雅英， 宮田孝富 - 電子情報通信学会技術研究報告. NLP ..., 2003 - ci.nii.ac.jp
  ... Affine Arithmetic (AA) is a kind of Interval Arithmetic (IA) proposed by Stolfi [3] in 1994. In this method, a quantity χ is represented by Affine form which we will mention in detail in the next ...
  

• Fine grain word length optimization for dynamic precision scaling in DSP systems
  S Lee, A Gerstlauer - ... on Very Large Scale Integration (VLSI ..., 2013 - ieeexplore.ieee.org
  ... Among the various analytical techniques, in [9] the authors adopt Affine Arithmetic (AA) to model the min/max error propagation of quantization noise. However, static min/max ...
  

• An Overflow/Underflow-Free Fixed-Point Bit-Width Optimization Method for OS-ELM Digital Circuit
  M Tsukada, H Matsutani - IEICE Transactions on Fundamentals of ..., 2022 - search.ieice.org
  ... represent OS-ELM in affine arithmetic. • Affine arithmetic can represent only fixed-length computation graphs and unbounded loops are not supported in affine arithmetic. However, OS-...
  

• Interval arithmetic and interval-aware operators for genetic programming
  G Dick - arXiv preprint arXiv:1704.04998, 2017 - arxiv.org
  ... Affine arithmetic has been proposed as an alternative to ... While we did not consider affine