Computer Algebra Support for the Completed Set of Intervals (original) (raw)

Towards a more complete interval arithmetic in Mathematica

Yilmaz Akyildiz

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Interval Arithmetic, Extended Numbers and Computer Algebra Systems

Richard Fateman

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Interval arithmetic: From principles to implementation

Tim Hickey

Journal of the ACM, 2001

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Theories of Interval Arithmetic: Mathematical Foundations and Applications

Hend Dawood

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Interval Computations and their

Nikolaj Glazunov

2003

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On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic

Hend Dawood

Online Mathematics Journal, 2019

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Interval Arithmetic. A practical implementation

Henrik Vestermark

2015

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Interval Mathematics: Foundations, Algebraic Structures, and Applications

Hend Dawood

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Formal Aspects of Correctness and Optimality of Interval Computations

Regivan Santiago

Formal Aspects of Computing, 2006

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Computation with the Extended Rational Numbers and an Application to Interval Arithmetic

Richard Fateman

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Non-linear extension of interval arithmetic and exact resolution of interval equations over square regions

Giovanny Andrés

arXiv (Cornell University), 2020

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Fundamentals of SIGLA, an interval computing system over the completed set of intervals

Albert Trepat

Computing, 1980

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On the Axiomatization of Interval Arithmetic

Svetoslav Markov

2005

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On the Evaluation of Rational Functions in Interval Arithmetic

Jon Rokne

SIAM Journal on Numerical Analysis, 1981

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Verified Real Number Calculations: A Library for Interval Arithmetic

Marc Daumas

Computing Research Repository, 2007

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Discussions on an Interval Arithmetic Standard at Dagstuhl Seminar 08021

R. Kearfott

Lecture Notes in Computer Science, 2009

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Algebraic Structures Using Natural Class of Intervals

Florentin Smarandache

2011

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Alternative Algebra for Multiplication and Inverse of Interval Number

Horizon Research Publishing(HRPUB) Kevin Nelson

Mathematics and Statistics, 2023

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The Mainstreaming of Interval Arithmetic

John Gustafson

Perspectives on Enclosure Methods, 2001

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Interval Computations and Their Categorification

Nikolaj Glazunov

Numerical Algorithms, 2004

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Universal Intervals: Towards a Dependency-Aware Interval Algebra

Hend Dawood, Yasser Dawood

Mathematical Methods in Interdisciplinary Sciences, 2020

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Interval Computations: Introduction, Uses, and Resources

R. Kearfott

1996

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Interval Mathematics as a Potential Weapon against Uncertainty

Hend Dawood

Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems, 2014

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Is an interval the right result of arithmetic operations on intervals?

Andrzej Piegat

International Journal of Applied Mathematics and Computer Science

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Towards a user transparent interval arithmetic

Jean-Michel Muller

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A unified framework for interval constraints and interval arithmetic

Tim Hickey

1998

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Is the conventional interval arithmetic correct?

Andrzej Piegat

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Interval-valued computations and their connection with

Benedek Nagy

Theoretical Computer Science, 2008

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WAI'96: II Workshop on Computer Arithmetic, Interval and Symbolic Computation

Marcilia Campos

Reliable Computing, 1996

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Algorithm 763; INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type

R. Kearfott

ACM Transactions on Mathematical Software, 1996

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Polynomial Precise Interval Analysis Revisited

Helmut Seidl

Lecture Notes in Computer Science, 2009

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A Review on Interval Computation–software and Applications

Chenyi Hu

Int. J. of Computational and Numerical Analysis and …, 2002

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