References in raw/Page_92.html

• Stabilizing floating-point programs using provenance analysis
  Y Gu, T Wahl - ... Conference on Verification, Model Checking, and ..., 2017 - Springer
  ... All these works use affine arithmetic [20] as the underlying algebraic structure to keep track of the rounding error. In this paper, we adopt a similar data structure, manifest in the ...
  

• Interval Tools in Branch-and-Bound Methods for Global Optimization
  J Fernández, B G-Tóth - The Palgrave Handbook of Operations Research, 2022 - Springer
  ... to minimize the range overestimation), the slope form [77] (where instead of inclusion of derivatives, inclusion of slopes are used), or the affine form [22] (which uses affine arithmetic ...
  

• Result Verification of RRT-based Single-Query Path Planning through Interval Analysis
  C Grimm - PAMM: Proceedings in Applied Mathematics and ..., 2008 - Wiley Online Library
  ... The deployment of Taylor arithmetic and affine arithmetic and their impact on the quality of the interval inclusions will be investigated in future work. The algorithm presented is an ...
  

• Range Analysis of Matrix Factorization Algorithms for an Overflow Free Fixed-point Design
  B Kabi, AS Sahadevan - Journal of Signal Processing Systems, 2019 - Springer
  ... Affine arithmetic (AA) is a preferable approach that takes into account the interdependency among the signals [19], but ranges determined through AA explode during division if the ...
  

• A reduced product of absolute and relative error bounds for floating-point analysis
  M Jacquemin, S Putot, F Védrine - International Static Analysis ..., 2018 - Springer
  ... In the fourth column of Table 1, we give the results of Fluctuat in its affine arithmetic based ... and errors, that combine interval and affine arithmetic based estimates with SMT. We included ...
  

• Differentiated local controls for distributed generators in active distribution networks considering cyber failures
  W Liu, Y Lu, M Yang, M Fu, L Wang - ... Journal of Electrical Power & Energy ..., 2022 - Elsevier
  ... The affine arithmetic could avoid situations where intervals ... Therefore, the interval power flow method based on affine arithmetic is ... based on the affine arithmetic is described as follows: ...
  

• An evaluation of pop performance for tuning numerical programs in floating-point arithmetic
  DB Khalifa, M Martel - 2021 4th International Conference on ..., 2021 - ieeexplore.ieee.org
  ... There are various rigorous static analysis approaches that use interval and affine arithmetic [19] or Taylor series approximations to analyze stability and to provide rigorous bounds on ...
  

• Automate convergence rate proof for gradient descent on quadratic functions
  Y Peng - cs.ubc.ca
  ... Their work on representing affine arithmetic fall into similar category of our work. But again, the kind of problems and properties are quite different. ...
  

• Transmission contingency-constrained unit commitment with high penetration of renewables via interval optimization
  Y Yu, PB Luh, E Litvinov, T Zheng... - ... on Power Systems, 2016 - ieeexplore.ieee.org
  ... generation through affine arithmetic [27], [28] in our approach. In affine arithmetic, the interval of ... Affine arithmetic has been shown to provide better bounds than the standard interval ...
  

• Power flow analysis under uncertainty using symmetric fuzzy arithmetic
  M Marin, D Defour, F Milano - 2014 IEEE PES General Meeting ..., 2014 - ieeexplore.ieee.org
  This paper present a novel approach using symmetric fuzzy numbers to deal with uncertainty in power system analysis. Special attention is put on reducing overestimation due to ...