References in raw/Page_71.html

• Improving ray tracing precision by object space intersection computation
  H Dammertz, A Keller - 2006 IEEE Symposium on Interactive ..., 2006 - ieeexplore.ieee.org
  ... Bounding intervals can be computed by interval or affine arithmetic [10, 13, 4], which is the ... However, each arithmetic operation then has to be performed in interval or affine arithmetic ...
  

• Using taylor models in exact real arithmetic
  F Brauße, M Korovina, N Müller - International Conference on ..., 2015 - Springer
  ... A further approach is affine arithmetic [5] which can be interpreted as a version of the Taylor ... arithmetic’ [8, 15] which is similar to affine arithmetic, but now with interval coefficients. ...
  

• Dynamical systems for arithmetic schemes
  C Deninger - arXiv preprint arXiv:1807.06400, 2018 - arxiv.org
  ... We begin with the case of an affine arithmetic scheme X0 = spec R0 and write X = spec R. Viewing • ... For a covering of X0 by open affine arithmetic subschemes Xi 0, the space ...
  

• Mathematical optimization in computer graphics and vision
  L Velho, P Carvalho, J Gomes, L De Figueiredo - 2011 - books.google.com
  ... Affine Arithmetic ... The role of interval and affine arithmetic in the solution to problems is also discussed. Applications to geometric modeling and animation are given. ...
  

• Optimization and anti-optimization solution of combined parameterized and improved interval analyses for structures with uncertainties
  R Santoro, G Muscolino, I Elishakoff - Computers & Structures, 2015 - Elsevier
  A novel method to deal with structures with uncertain-but-bounded parameters is presented. In order to reduce or eliminate the overestimations due to the so-called dependency ...
  

• Precision analysis with analytical bit-width optimisation process for linear circuits with feedbacks
  ES Lamini, S Tagzout, H Belbachir... - IET Circuits, Devices ..., 2018 - Wiley Online Library
  ... Authors in [25, 26] use the affine arithmetic (AA) for the same reason. Interval arithmetic (IA) approach establishes worst case bounds on each intermediate step of the calculation by ...
  

• The small octagons of maximal width
  C Audet, P Hansen, F Messine, J Ninin - Discrete & Computational ..., 2013 - Springer
  ... This linear relaxation are generated using an extension of affine arithmetic [12, 14]. To ensure the numerical reliability of the solutions provided by a linear solver (here, we used CPLEX)...
  

• Robustness analysis of finite precision implementations
  E Goubault, S Putot - Asian Symposium on Programming Languages and ..., 2013 - Springer
  ... Affine arithmetic is a more accurate extension of interval arithmetic, that takes into account affine correlations between variables. An affine form is a formal sum over a set of noise ...
  

• New fast algorithms for arithmetic on elliptic curves over fields of characteristic three
  KH Kim, SI Kim, JS Choe - Cryptology ePrint Archive, 2007 - eprint.iacr.org
  In previous works on ECC (Elliptic Curve Cryptography), the case of characteristic three has been considered relatively less than cases of fields of even characteristic and large prime ...
  

• Polygonal surface advection applied to strange attractors
  S Yan, N Max, KL Ma - Computer Graphics Forum, 2010 - Wiley Online Library
  ... [[PdFS06]] visualize 2D strange attractors using affine arithmetic, which gives tighter bounds than interval arithmetic. Rössler [[Rös76]] discovered a simpler system of three ODEs, ...