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 …

[HTML][HTML] 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 …

[HTML][HTML] 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 …

[PDF][PDF] 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 …