References in raw/Page_39.html

• An interval power flow for unbalanced distribution systems based on the Three-Phase Current Injection Method
  HMR Junior, ID Melo, EG Nepomuceno - International Journal of Electrical ..., 2022 - Elsevier
  ... work is the proposition of two methods based on traditional interval arithmetic to reduce the diameter of the solution and achieve similar results when compared with Affine Arithmetic ...
  

• Towards implementing uncertainty propagation in probabilistic floating-point computation error bounding
  R Zhang, A Rajan, YC Kuang, MPL Ooi... - 2018 IEEE ..., 2018 - ieeexplore.ieee.org
  ... bounds instead of mathematically guaranteed bounds, the tightness of the bounds can be substantially improved compared to the mainstream interval arithmetic and affine arithmetic ...
  

• Extended component importance measures considering aleatory and epistemic uncertainties
  M Sallak, W Schon, F Aguirre - IEEE Transactions on Reliability, 2013 - ieeexplore.ieee.org
  ... Affine arithmetic allows us to provide much tighter bounds in the computing process of interval bounds of importance measures, avoiding the error explosion problem. The efficiency of ...
  

• Processing Measurement Uncertainty: From Intervals and p-Boxes to Probabilistic Nested Intervals
  KK Semenov, GN Solopchenko, V Kreinovich - 2012 - konf.ict.nsc.ru
  → Conclusion. Classical interval techniques (Moore’s arithmetic, affine arithmetic etc) can be used for systematic errors propagating (but, of course, if we use interval methods for ...
  

• Synthesis of fixed-point programs
  E Darulova, V Kuncak, R Majumdar... - 2013 Proceedings of the ..., 2013 - ieeexplore.ieee.org
  ... , we use a static analysis based on affine arithmetic to compute an upper bound on the error. ... limitations in using static analysis based on affine-arithmetic, but our search method works ...
  

• A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling
  E Dyllong - Dagstuhl Seminar Proceedings, 2008 - drops.dagstuhl.de
  ... The utilization of affine arithmetic and other improved techniques of reliable computing in the field of modeling can be found in [3,4]. For moving multibody models a continuous collision ...
  

• Dynamic response analysis of structure under time-variant interval process model
  B Xia, Y Qin, D Yu, C Jiang - Journal of Sound and Vibration, 2016 - Elsevier
  ... To solve the dependency phenomenon of the interval operation, the affine arithmetic is integrated into the Chebyshev polynomial expansion. The computational effectiveness and ...
  

• A recursive Taylor method for algebraic curves and surfaces
  H Shou, R Martin, G Wang, A Bowyer... - ... Methods for Algebraic ..., 2005 - Springer
  ... less accurate than a modified affine arithmetic method (MAA) ... showed that the modified
  

• Symbolic analysis of the Tau Cell log-domain filter using affine MOSFET models
  B Thanigaivelan, A Postula, C Jin... - 2010 IEEE Asia ..., 2010 - ieeexplore.ieee.org
  ... we developed and used to analyse the Tau Cell is based on affine arithmetic concepts and overcomes the difficulties mentioned above. An affine arithmetic number can be defined as, ...
  

• On the Automatic Computation of Error Bounds for Solutions of Nonlinear Equations
  E Darulova, V Kuncak - 2012 - infoscience.epfl.ch
  ... affine arithmetic, although the latter is usually presented as the superior approach. Indeed, for the tracking of roundoff errors we have shown affine arithmetic ... , since affine arithmetic has ...