References in raw/Page_62.html

-
DynBEX: a Differential Constraint Library for Studying Dynamical Systems
JAD Sandretto, A Chapoutot - Conference on Hybrid ..., 2016 - hal.archives-ouvertes.fr
... To avoid some limitations with interval arithmetic, other kinds of arithmetic may bu used such
as affine arithmetic [3]. Both arithmetic are available in IBEX. Consider some function g : Rn ...
Mathematics of Surfaces: 10th IMA International Conference, Leeds, UK, September 15-17, 2003, Proceedings
MJ Wilson - 2003 - books.google.com
... , extracting shape form shading, surface height recovery, reverse engineering, box-splines,
the Plateau Problem, splines (a variety of papers), transfinite blending, and affine arithmetic. ...
Interactive ray tracing of arbitrary implicits with simd interval arithmetic
A Knoll, Y Hijazi, C Hansen, I Wald... - 2007 IEEE Symposium ..., 2007 - ieeexplore.ieee.org
... a higher-order inclusion rule set such as affine arithmetic [3] or midpoint-Taylor arithmetic [7].
... Interval methods for raycasting implicit surfaces with affine arithmetic. In Proceedings of XII ...
Towards program optimization through automated analysis of numerical precision
MD Linderman, M Ho, DL Dill, TH Meng... - Proceedings of the 8th ..., 2010 - dl.acm.org
... )-based proof engine with an affine arithmetic (AA)-based engine that can more accurately
... Affine arithmetic (AA) [9] is a refinement to IA that addresses the above problem by keeping ...
Sound Probabilistic Numerical Error Analysis
SIC MPI-SWS - Integrated Formal Methods LNCS 11918 - Springer
... Affine arithmetic represents a range of possible values by an ... Probabilistic Affine Arithmetic
The worst-case error can be ... probability distributions is probabilistic affine arithmetic [4]. Here, ...
Inner and outer approximating flowpipes for delay differential equations
E Goubault, S Putot, L Sahlmann - International Conference on Computer ..., 2018 - Springer
... We evaluate it in interval rather than affine arithmetic for simplicity: \([\varvec{F}](\varvec{x})=
1 + [0,\frac{1}{3}] \left( 1+[\frac{1}{3},1] [-1,-\frac{2}{3}]\right) ^2 \varvec{x}= 1 + [0,\frac{7^2}{3^5...
Computing flowpipe of nonlinear hybrid systems with numerical methods
O Bouissou, A Chapoutot, S Mimram - arXiv preprint arXiv:1306.2305, 2013 - arxiv.org
... In this section, we first briefly present our encoding of sets using affine arithmetic (Section
3.1) and show how explicit Runge-Kutta like numerical integration methods (Section 3.2) and ...
Reliable algorithms for ray intersection in computer graphics based on interval arithmetic
JF Sanjuan-Estrada, LG Casado... - ... Brazilian Symposium on ..., 2003 - ieeexplore.ieee.org
... mance of affine arithmetic as a replacement of interval arithmetic in interval methods for ray
tracing implicit surfaces. In this work we analyze and evaluate the algorithms developed by ...
Application of differential evolution-based constrained optimization methods to district energy optimization and comparison with dynamic programming
S Ikeda, R Ooka - Applied Energy, 2019 - Elsevier
Metaheuristic optimization methods, as model-free approaches, are expected to be applicable
to practical issues (eg, engineering problems). Although optimization methods have been ...
Analytical approach for numerical accuracy estimation of fixed-point systems based on smooth operations
R Rocher, D Menard, P Scalart... - IEEE Transactions on ..., 2012 - ieeexplore.ieee.org
... throughout the system thanks to an affine arithmetic based simulation. The values of ...
Nevertheless, in the case of recursive systems, several iterations for the affine arithmetic based ...