References in raw/Page_46.html

• Range Based Analysis of Inner Systems Characteristics
  M Rathmair - publik.tuwien.ac.at
  ... -symbolic calculation methodology based on Affine Arithmetic is used. Abstract symbols describe ... An object oriented implementation of an Affine Arithmetic datatype and corresponding ...
  

• Certified meshing of Radial Basis Function based isosurfaces
  A Chattopadhyay, S Plantinga, G Vegter - The Visual Computer, 2012 - Springer
  ... Our early experiments show that even the straightforward use of affine arithmetic (AA) [7], a fine tuned version of IA, does not improve running times sufficiently. Therefore, we developed ...
  

• Modeling, Simulation and Uncertain Optimization of the Gun Engraving System
  T Xin, G Yang, F Xu, Q Sun, A Minak - Mathematics, 2021 - mdpi.com
  ... method based on affine arithmetic is adopted, and the phrase “affine arithmetic-based method” is ... Second, the affine arithmetic is utilized to obtain the interval of objective function and ...
  

• Visualizing nonmanifold and singular implicit surfaces with point clouds
  RJ Balsys, DJ Harbinson... - IEEE Transactions on ..., 2011 - ieeexplore.ieee.org
  ... approach than with the use of interval or affine arithmetic exclusion tests. This is evident in Figs. ... Compared to interval pruning the interval and affine arithmetic approaches produce poor ...
  

• Toward a standard benchmark format and suite for floating-point analysis
  N Damouche, M Martel, P Panchekha, C Qiu... - ... Workshop on Numerical ..., 2016 - Springer
  ... Rosa [11] combines an exact SMT solver on reals with sound affine arithmetic to verify accuracy post-conditions from assertions about the accuracy of inputs. Rosa can guarantee that ...
  

• Tracing harmonic distortion and voltage unbalance in secondary radial distribution networks with photovoltaic uncertainties by an iterative multiphase ...
  JC Hernandez, FJ Ruiz-Rodriguez, F Jurado... - Electric Power Systems ..., 2020 - Elsevier
  ... This technique merges the point-estimate method (PEM) and complex affine arithmetic (AA), combined with Legendre series approximation (LGSA). It also models the input correlation. ...
  

• Formally verified computation of enclosures of solutions of ordinary differential equations
  F Immler - NASA Formal Methods Symposium, 2014 - Springer
  ... We define a function ˆQ using affine arithmetic to overapproximate Q. Then we iterate ˆQpr, starting with box p X0, until we find a post fixed point. That means when we encounter boxes ...
  

• Uncertainty Updating of Finite Element Models Using Interval Analysis
  D Shan, YH Chai, H Dong, Z Li - International Journal of Structural ..., 2020 - World Scientific
  ... affine arithmetic into finite element updating, as motivated by the understanding of affine
  

• Special section on recent progress in verified numerical computations
  T Ogita, K Ozaki, SM Rump - Nonlinear Theory and Its Applications ..., 2015 - jstage.jst.go.jp
  ... Rump and Masahide Kashiwagi is concerned with affine arithmetic, which can reduce the wrapping effect of naive interval arithmetic. On the regular papers, the following variety of ...
  

• Quantifying the effects of uncertainty in building simulation
  IA Macdonald - 2002 - esru.strath.ac.uk
  ... Three methods were studied: interval, fuzzy and affine arithmetic. It was found when forming the energy balance equation set, correlations between the source of uncertainty and the ...