Certification of a Numerical Result: Use of Interval Arithmetic and Multiple Precision Hong Diep Nguyen and Nathalie Revol INRIA Universit´e de Lyon Laboratoire LIP (UMR 5668 CNRS - ENS Lyon - INRIA - UCBL)

Source URL: perso.ens-lyon.fr

• Numerical analysis
• Mathematics
• Applied mathematics
• Iterative refinement
• Iterative method
• Interval arithmetic
• Newton's method
• Condition number
• Residual
• Root-finding algorithm
• Affine arithmetic

Introduction to the IEEEStandard for Interval Arithmetic

Source URL: www.cs.ox.ac.uk

• Computer arithmetic
• Mathematics
• Numerical analysis
• Arithmetic
• Interval arithmetic
• Interval

1 Interval Analysis and Machine Arithmetic: Why Signedness Ignorance Is Bliss GRAEME GANGE, JORGE A. NAVAS, PETER SCHACHTE, HARALD SØNDERGAARD, and PETER J. STUCKEY, The University of Melbourne, Australia

Source URL: jorgenavas.github.io

• Mathematics
• Computer arithmetic
• Algebra
• Abstract algebra
• Abstract interpretation
• Interval arithmetic
• Two's complement
• Interval
• Signedness
• Logarithm
• Modular arithmetic
• Division by zero

Doc No: N2137=A Proposal to add Interval Arithmetic to the C++ Standard Library (revision 2) Hervé Brönnimann∗

Source URL: www.open-std.org

Function Interval Arithmetic Jan Duracz1 , Amin Farjudian2 , Michal Koneˇcný3 , and Walid Taha4 1 , http://duracz.net/jan

Source URL: duracz.net

BIT Numerical Mathematics, 52(4):1059–1075, 2012 INTERVAL ARITHMETIC OVER FINITELY MANY ENDPOINTS SIEGFRIED M. RUMP ∗

Source URL: www.ti3.tu-harburg.de

Users’ manual for the Sollya tool Release 5.0 Sylvain Chevillard Christoph Lauter

Source URL: gforge.inria.fr

• Mathematics
• Arithmetic
• Computer arithmetic
• Mathematical analysis
• Subroutines
• Theoretical computer science
• Data types
• Numerical analysis
• Rounding
• Parameter
• Derivative
• Interval arithmetic

P1788 – Standardization of Interval Arithmetic Vincent LEFÈVRE AriC, INRIA Grenoble – Rhône-Alpes / LIP, ENS-Lyon GdT AriC,

Source URL: www.vinc17.org

• Mathematics
• Computer arithmetic
• Arithmetic
• Numerical analysis
• Interval arithmetic
• Interval
• Rounding
• Real number

Verified solutions of sparse linear systems Takeshi Ogita Division of Mathematical Sciences, Tokyo Woman’s Christian University 2–6–1 Zempukuji, Suginami-ku, Tokyo 167–8585, Japan

Source URL: conf.nsc.ru

• Mathematics
• Numerical analysis
• Applied mathematics
• Numerical linear algebra
• Matrix
• Academia
• Interval arithmetic
• Sparse matrix

BIT 39(3), pp. 539–560, 1999 FAST AND PARALLEL INTERVAL ARITHMETIC SIEGFRIED M. RUMP Inst. of Computer Science III, Technical University Hamburg-Harburg, Eißendorfer Str. 38, 21071 Hamburg, Germany.

Source URL: www.ti3.tu-harburg.de

• Mathematics
• Computer arithmetic
• Mathematical logic
• Theory of computation
• Numerical analysis
• Arithmetic
• Interval arithmetic
• Interval
• Constructible universe
• Ordinal number
• NC
• Machine epsilon