PCU: the programmable culling unit

J Hasselgren, T Akenine-Möller - ACM SIGGRAPH 2007 papers, 2007 - dl.acm.org
… reasons for discarding affine arithmetic (apart … affine arithmetic, and that the texture lookups
instantly break all linear dependencies. We did some preliminary tests using affine arithmetic

A fast and flexible accuracy-guaranteed fractional bit-widths optimization approach

L Zhang, Y Zhang, W Zhou - 2009 IEEE International …, 2009 - ieeexplore.ieee.org
… [5] use Affine Arithmetic (AA), which considers the correlations among signals, to model
range and precision analyses. However range and precision are solved in one single affine …

Extended analysis of a damage prognosis approach based on interval arithmetic

C Surace, K Worden - Strain, 2011 - Wiley Online Library
… to interval arithmetic, termed affine arithmetic [15], which, in many … Another advantage of
affine arithmetic is the inclusion of an … The use of affine arithmetic for prognosis purposes will be …

[PDF][PDF] A solution algorithm for a system of interval linear equations based on the constraint interval point of view

M Keyanpour, M Taber, W Lodwick - Realible Comput, 2018 - interval.louisiana.edu
… There, in particular, affine arithmetic of [13] is discussed. In [5] many types of interval arithmetics
are discussed, not just affine arithmetic. Affine arithmetic deals with dependencies via a …

An Introduction to Proofs with Set Theory

D Ashlock, C Lee - Synthesis Lectures on Mathematics and …, 2020 - morganclaypool.com
This text is intended as an introduction to mathematical proofs for students. It is distilled from
the lecture notes for a course focused on set theory subject matter as a means of teaching …

[BOOK][B] A reliable affine relaxation method for global optimization

J Ninin, P Hansen, F Messine - 2010 - optimization-online.org
… In this paper, the main idea is to use affine arithmetic [4… as for interval arithmetic, affine
arithmetic can be implemented in … recalls basic definitions about affine arithmetic and affine forms. …

[HTML][HTML] An interval sequential linear programming for nonlinear robust optimization problems

J Tang, C Fu, C Mi, H Liu - Applied Mathematical Modelling, 2022 - Elsevier
… Wang and Qing [30] utilized mixed interval arithmetic and affine arithmetic method to
obtain affine approximations of the objective function and constraints to transform the robust …

Inner regions and interval linearizations for global optimization

G Trombettoni, I Araya, B Neveu… - Proceedings of the AAAI …, 2011 - ojs.aaai.org
… Ninin et al. were guided to this choice by their affine arithmetic, but we believe that this is
a relevant approach for any global optimization solver. First, both policies are of equal status …

Introduction to the Special Section on Computer Arithmetic

J Hormigo, JM Muller, S Obermann… - IEEE Transactions …, 2017 - hal.archives-ouvertes.fr
… encompass interval arithmetic, algorithms and applications and related topics such as the
use of floating-point arithmetic for implementation issues, variants such as affine arithmetic or …

[PDF][PDF] Networked adaptive classification for cyber-physical systems

M Gilberti - 2011 - dspace.sunyconnect.suny.edu
Affine Arithmetic is used to optimize both the range and precision of the fixed-point numbers.
Affine Arithmetic is … The difference between the two is that Affine Arithmetic uses a separate …