# Introduction to Interval Analysis

@inproceedings{Moore2009IntroductionTI, title={Introduction to Interval Analysis}, author={Ramon E. Moore and Ralph Baker Kearfott and Michael J. Cloud}, year={2009} }

This unique book provides an introduction to a subject whose use has steadily increased over the past 40 years. An update of Ramon Moore s previous books on the topic, it provides broad coverage of the subject as well as the historical perspective of one of the originators of modern interval analysis. The authors provide a hands-on introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB…

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## 1,911 Citations

16w5099—INTERVAL ANALYSIS AND CONSTRUCTIVE MATHEMATICS

- Mathematics
- 2017

In this case, we have two fields to overview—constructive mathematics and interval analysis—one of the main objectives of the workshop being to foster joint research across the two. By ‘constructive…

New Package in Maxima for Single-Valued Interval Computation on Real Numbers

- Computer Science, Mathematics2011 International Conference on Computational Science and Its Applications
- 2011

A new package for dealing with single-valued interval computation on real numbers, developed by the authors in free ware program Maxima, version 5.23.2, allows the user to manipulate single- valued real and extended intervals and carry out the most typical set operations on intervals in a smoothly and user-friendly way.

Bounds from Slopes

- Computer Science
- 2010

Sometimes it is desirable to compute good bounds on the possible values of an algebraic expression involving variables only known to lie in prescribed finite intervals. While interval arithmetic…

Latest Developments on the IEEE 1788 Effort for the Standardization of Interval Arithmetic

- Computer Science
- 2014

The structure of the proposed standard is presented: the mathematical level is distinguished from both the implementation and representation levels, and a tentative list of missing items is given.

Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)

- Computer ScienceDagstuhl Reports
- 2011

This work seeks to implement a minimal interval arithmetic by generating code on the fly using MPFR, and should be as simple as possible so that it could easily be checked and/or proved formally.

Interval Analysis and Calculus for Interval-Valued Functions of a Single Variable. Part I: Partial Orders, gH-Derivative, Monotonicity

- Mathematics, Computer ScienceAxioms
- 2019

A new general setting for partial order in the (semi linear) space of compact real intervals and corresponding concepts for the analysis and calculus of interval-valued functions of a single real variable are developed.

Verification methods: Rigorous . . .

- Computer Science
- 2010

One main goal of this review article is to introduce the principles of the design of verification algorithms, and how these principles differ from those for traditional numerical algorithms.

Computer-aided proofs and algorithms in analysis

- Computer Science
- 2013

Further applications of those two basic ideas, namely interval arithmetic and automatic differentiation, that address the question of the reliability of the results and the difficulty of calculating derivatives are presented.

Semi-Automatic Analysis of Algorithm Complexity (Case Study: Square-Root Computation)

- Computer Science
- 2014

This paper overcame the difficulty by carefully reducing a complicated quantified formula into several simpler ones and automatically eliminating the quantifiers from the resulting ones using the state-of-the-art quantifier elimination software, and was able to compute semi-automatically the complexity of a class of optimal contracting maps.

Interval Mathematics: Foundations, Algebraic Structures, and Applications

- Mathematics
- 2012

Student Name: Hend Dawood Mohamed. Thesis Title: Interval Mathematics: Foundations, Algebraic Structures, and Applications. Degree: Master of Science in Computer Science. We begin by constructing the…

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