References in raw/Page_49.html

• A reliable algorithm for computing the topological degree of a mapping in R2
  KH Ko, T Sakkalis, NM Patrikalakis - Applied Mathematics and ..., 2008 - Elsevier
  ... In Section 2, we briefly review interval and affine arithmetic and its extension to complex arithmetic. In Section 3, we propose an adaptive discretization method for condition (8) and ...
  

• Zonotopic Filtering for Uncertain Nonlinear Systems: Fundamentals, Implementation Aspects, and Extensions [Applications of Control]
  AA de Paula, GV Raffo... - IEEE Control Systems ..., 2022 - ieeexplore.ieee.org
  ... In parallel to interval arithmetic (IA), many contributions were addressed for affine arithmetic since more general sets than boxes can be defined. In this context, the parallelotopes ...
  

• Validated explicit and implicit Runge-Kutta methods
  JAD Sandretto, A Chapoutot - ... Computing electronic edition, 2016 - hal.archives-ouvertes.fr
  ... We provide also an approach based on affine arithmetic [14], in the same spirit than [23], in order to increase the width of initial values while keeping low complexity on arithmetic ...
  

• Simulation and verification of hybrid systems using hyson
  O Bouissou, A Chapoutot... - ... International Workshop on ..., 2014 - lix.polytechnique.fr
  ... In order to represent sets of reals, we use affine arithmetic [9]: it is a refinement over interval arithmetic [18] which is able to keep track of linear correlations between variables. A set of ...
  

• MESTRADO EM ENGENHARIA ELÉTRICA
  AIAÀS DO, FDEPVIAE DE, I DE CORRENTE - repositorio.ufjf.br
  ... , based on the use of affine arithmetic. This alternative technique has been developed to improve the self-validated numerical analysis. Within affine arithmetic, the quantities of interest ...
  

• Sound compilation of reals
  E Darulova, V Kuncak - Proceedings of the 41st ACM SIGPLAN-SIGACT ..., 2014 - dl.acm.org
  ... For completeness of presentation, we first review interval and affine arithmetic which are ... that can be a more precise substitute for interval or affine arithmetic. Finally, we continue with a ...
  

• Evaluation of Distributed Generation and Electric Vehicles Hosting Capacity in Islanded DC Grids Considering EV Uncertainty
  CD Zuluaga-Ríos, A Villa-Jaramillo... - Energies, 2022 - mdpi.com
  ... The authors in [11] proposed a method based on iterative sweep load flow and affine arithmetic ... For example, [28] proposed to use interval and affine arithmetic, power flow computation ...
  

• ReLU Neural Networks of Polynomial Size for Exact Maximum Flow Computation
  C Hertrich, L Sering - arXiv preprint arXiv:2102.06635, 2021 - arxiv.org
  ... To study them as a model of real-valued computation, we introduce the concept of Max-Affine
  

• Affine-Type Model of Variable Renewable Energy and Its Application in the Uncertain Power Flow
  G Huang, Z Shao, Y Zhang - Journal of Physics: Conference ..., 2020 - iopscience.iop.org
  ... It is essential to develop the affine arithmetic to improve the ... For instance, an affine
  

• Explicit reliability sensitivities of linear structures with interval uncertainties under stationary stochastic excitation
  G Muscolino, R Santoro, A Sofi - Structural Safety, 2015 - Elsevier
  ... Following the philosophy of the affine arithmetic, within the framework of structural analysis, the so-called improved interval analysis via extra unitary interval has been proposed [30], [33...