References in raw/Page_45.html

• Static analysis by abstract interpretation: A mathematical programming approach
  E Goubault, S Le Roux, J Leconte, L Liberti... - Electronic notes in ..., 2010 - Elsevier
  ... Although we limit the discussion to integer affine arithmetic semantics in the interval domain, the flexibility and power of mathematical programming tools have the potential for enriching ...
  

• Convex Interval Taylorization in Constrained Global Optimization
  I Araya, G Trombettoni, B Neveu - www-sop.inria.fr
  ... this affine arithmetic and our corner-based taylorization. ... Compared to affine arithmetic, first experiments suggest that our ... has the potential to complement affine arithmetic and Quad. ...
  

• A Review of Interval Field Approaches for Uncertainty Quantification in Numerical Models
  M Faes, M Imholz, D Vandepitte... - Modern Trends in ..., 2021 - Wiley Online Library
  ... The methods based on affine arithmetic integrate well with the well-known KL expansion method, allowing for the application of a globally defined homogeneous auto-dependence ...
  

• Quantization analysis of the infrared interferometer of the tj-ii stellarator for its optimized fpga-based implementation
  L Esteban, JA López, E Sedano... - ... on Nuclear Science, 2013 - ieeexplore.ieee.org
  ... In [7], the temporal correlation problem of Affine Arithmetic is solved by including all the terms with ... However, since the applied analytical method is Affine Arithmetic, the treatment of the ...
  

• A Contractor based on Convex Interval Taylorization
  I Araya, G Trombettoni, B Neveu - www-sop.inria.fr
  ... Compared to affine arithmetic, preliminary experiments suggest that our convex interval ... reliable convexification method has the potential to complement affine arithmetic and Quad. ...
  

• Proteins Structure Determination with Imprecise Distances
  I Sendin, SK Goldenstein - Proceedings of DGA, 2013 - ic.unicamp.br
  ... Affine arithmetic ensures that the resulting affine form contains the true value provided that the operands contain the true value. This property, useful for reliable computing, in general is ...
  

• Reliable distance and intersection computation using finite precision geometry
  K Bühler, E Dyllong, W Luther - Numerical Software with Result Verification, 2004 - Springer
  ... They are constructed using Taylor models or affine arithmetic. The particular structure of (I)LIEs allows the construction of effective hierarchies of bounding volumes and the ...
  

• Solution proposal to the unit commitment problem incorporating manifold uncertainties
  F Zhai, L Shi - IET Generation, transmission & distribution, 2020 - researchgate.net
  ... Furthermore, the uncertainty of power loss is considered and modeled by applying the ET and the extended affine arithmetic framework. Regarding the highly nonlinear mix-discrete ...
  

• Implicit linear interval estimations
  K Bühler - Proceedings of the 18th spring conference on ..., 2002 - dl.acm.org
  ... This section requires some basic knowledge about interval and affine arithmetic. A short ... way is to use affine arithmetic: Like in the straight forward use of affine arithmetic for cell/object in...
  

• Instrumentation of the Control Flow of SystemC AMS-Models for Symbolic Simulation
  C Radojicic, C Grimm - ANALOG 2016; 15. ITG/GMM ..., 2016 - ieeexplore.ieee.org
  ... In Section 2 we give an overview of the symbolic simulation based on Extended Affine Arithmetic. ... with Extended Affine Arithmetic. The demonstration example is described in Section 5. ...