References in raw/Page_65.html

• Static analysis of the accuracy in control systems: Principles and experiments
  E Goubault, S Putot, P Baufreton, J Gassino - International Workshop on ..., 2007 - Springer
  ... We thus proposed and implemented a relational domain, relying on affine arithmetic [5,22] ... The real part is computed using affine arithmetic, and the error is computed using three ...
  

• Analysis of fixed-point singular value decomposition algorithms
  B Kabi - Master's thesis, 2015 - researchgate.net
  ... Affine arithmetic is an improvement over interval arithmetic that takes correlation between ... If affine form of x is x=x0 + x1ε1, the operation y=x − x performed in affine arithmetic would ...
  

• Interval-valued statistical modeling of oxide chemical-mechanical polishing
  JD Ma, CF Fang, RA Rutenbar, X Xie... - ICCAD-2005. IEEE ..., 2005 - ieeexplore.ieee.org
  ... The affine arithmetic library and the four interval-valued statistical CMP modeling algorithms have been implemented in C/C++ and tested on a 1.0GHz UNIX machine using two layout ...
  

• Segment tracing using local lipschitz bounds
  E Galin, E Guérin, A Paris... - Computer Graphics ..., 2020 - Wiley Online Library
  ... A complete comparison between Lipschitz techniques and interval analysis using Interval Affine [Mit90] or Affine Arithmetic [GM07] is beyond the scope of this paper. Still, binary search ...
  

• Probabilistic load flow calculation using cumulants and multiple integrals
  W Wu, K Wang, G Li, X Jiang... - IET Generation ..., 2016 - Wiley Online Library
  ... Reliable power flow calculation using affine arithmetic is another interval analysis tool where each uncertainty is represented as affine combinations of certain primitive variables [1, 2]. It ...
  

• Reliability Evaluation of Repairable Parallel-Series Multi-State System Implementing Interval Valued Universal Generating Function
  S Bisht, SB Singh - Journal of Reliability and ..., 2021 - journal.riverpublishers.com
  ... In this study, they discussed the reliability of the system and affine arithmetic to improve interval-valued reliability using the imprecise Dirichlet model and Bayesian approach. Lisnianski ...
  

• A framework to explore low-power architecture and variability-aware timing estimation of FPGAs
  LEEC SING - 2007 - core.ac.uk
  ... special acknowledgment to Professor Jonathan Rose and Vaughn Betz (creators of VPR tool) from the University of Toronto as well as Professor Jorge Stolfi (creator of affine arithmetic ...
  

• Efficient search for inputs causing high floating-point errors
  WF Chiang, G Gopalakrishnan, Z Rakamaric... - Proceedings of the 19th ..., 2014 - dl.acm.org
  ... We can observe that both interval and affine arithmetic tools, namely Gappa and SmartFloat, returned overly pessimistic results. We manually calculated the range of the outputs and ...
  

• Formally verified roundoff errors using SMT-based certificates and subdivisions
  J Bard, H Becker, E Darulova - International Symposium on Formal ..., 2019 - Springer
  ... Verifying SMT-based results also allowed us to compute and verify a roundoff error for the JetEngine benchmark, for which interval and affine arithmetic report a spurious division by ...
  

• Verified analysis of a model for stance stabilization
  E Auer, H Albassam, A Kecskeméthy... - Modeling, Design, and ..., 2011 - Springer
  ... Interval [19], Taylor model [17] or affine arithmetic [6] based methods are most prominent examples of verified techniques. Besides proving the correctness of the computed result, ...