References in raw/Page_71.html

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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, ...