References in raw/Page_77.html

• On auto-and cross-interdependence in interval field finite element analysis
  M Faes, D Moens - International Journal for Numerical Methods ..., 2020 - Wiley Online Library
  ... element-by-element approaches11 or affine arithmetic.13 A second challenge lies in the ... more recently by other authors based on affine arithmetic,17, 18 a spatial averaging method,...
  

• Conic optimization method for voltage stability assessment of active distribution networks with different wind turbine models
  J Tong, C Chang, W Kaiyao - International Journal of Electrical Power & ..., 2022 - Elsevier
  This paper presents a conic optimization method based on Semi-Definite Programming (SDP) relaxation for calculating the Static Voltage Stability Limitation (SVSL) in Active ...
  

• A bit too precise? Bounded verification of quantized digital filters
  A Cox, S Sankaranarayanan, BYE Chang - ... on Tools and Algorithms for the ..., 2012 - Springer
  ... We perform an error analysis to show that such an overapproximation can be addressed using affine arithmetic simulations [6] or BMC using linear real arithmetic constraints (Section 4)...
  

• A scalable approach for automated precision analysis
  D Boland, GA Constantinides - Proceedings of the ACM/SIGDA ..., 2012 - dl.acm.org
  ... When performing polynomial approximations, for a fair comparison we use the same polynomial approximation method for affine arithmetic and our approach, with the exception of ...
  

• Gödel, constructivity, impredicativity, and feasibility
  J Fichot - One Hundred Years of Intuitionism (1907–2007), 2008 - Springer
  ... definable in Bellantoni and Cook’s system are provably total in epistemic affine arithmetic: ... in epistemic affine arithmetic are polytime computable by a term typed in Hofmann’s system. ...
  

• Interval arithmetic power flow analysis of radial distribution system including uncertainties in input parameters
  SS Parihar, N Malik - 2017 7th International Conference on ..., 2017 - ieeexplore.ieee.org
  ... Authors in [10] proposed an Affine Arithmetic approach to handle uncertainties. The method is independent of the types and level of uncertainties in the input data. Similar work is done ...
  

• Towards Faster Estimation of Statistics and ODEs under Interval, P-Box, and Fuzzy Uncertainty: From Interval Computations
  V Kreinovich - cs.utep.edu
  ... Affine arithmetic: we start with x = 0.5 − ∆x + [0,0]; • r1 := 1 − (0.5 − ∆) = 0.5+∆x; • r2 := (0.5 − ∆x) · (0.5+∆x), ... Accuracy: affine arithmetic leads to more accurate ranges. • Computation time: ...
  

• A Taylor model toolbox for solving ODEs implemented in MATLAB/INTLAB
  F Bünger - Journal of Computational and Applied Mathematics, 2020 - Elsevier
  ... For the special case of degree m = 1 , standard domain D s , and center point c s this coincides with the enclosure represented by an object in affine arithmetic with k error terms. ...
  

• Discovering affine equalities using random interpretation
  S Gulwani, GC Necula - Proceedings of the 30th ACM SIGPLAN ..., 2003 - dl.acm.org
  ... The language of expressions that we have considered so far allows only for affine arithmetic expressions. In this section we speculate about the uses of randomized algorithms for ...
  

• Fine-grained floating-point precision analysis
  MO Lam, JK Hollingsworth - The International Journal of ..., 2018 - journals.sagepub.com
  ... 4.2 Interval and affine arithmetic ... (1994) and others with the concept of “affine arithmetic,” replacing the ranges of interval arithmetic with a linear combination of error factors. Affine ...