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
Highly Influential Citations
105
Background Citations
517
Methods Citations
346
Results Citations
7

1,911 Citations

16w5099—INTERVAL ANALYSIS AND CONSTRUCTIVE MATHEMATICS
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
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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
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
TLDR
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)
TLDR
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
TLDR
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 . . .
TLDR
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
TLDR
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)
TLDR
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
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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References

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extremely leisurely. In fact, a professional analyst can sometimes become a little impatient, but of course the book is addressed to the entirely inexperienced beginner. Chapter II finishes on p.…
Interval Analysis in Matlab
TLDR
Interval arithmetic is used to take account of rounding errors in the computation of Viswanath's constant, the rate at which a random Fibonacci sequence increases.
Taylor Forms—Use and Limits
This review is a response to recent discussions on the reliable computing mailing list, and to continuing uncertainties about the properties and merits of Taylor forms, multivariate higher degree…
Classical and Modern Numerical Analysis: Theory, Methods and Practice
TLDR
This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area.
On solving systems of equations using interval arithmetic
Introduction. In this paper, we consider the problem of applying interval arithmetic to bound a solution of a system of nonlinear equations. Moore [1, Section 7.3] has discussed the same problem. His…
Interval Arithmetic with Containment Sets
TLDR
Basic theory of containment sets is presented, the case for a global flag to support ``loose'' evaluation, performance, and semantics are discussed, and numerical examples using a trial Matlab implementation are presented.
Accuracy and Reliability in Scientific Computing
TLDR
This book is a collection of 13 articles dealing with accuracy and reliability of scientific computing, and the overall theme of the book is the increasingly critical problem of reliability in technical computing.
Algorithm 763: INTERVAL_ARITHMETIC: a Fortran 90 module for an interval data type
TLDR
The Fortran 90 module INTERVAL_ARITHMETIC provides a portable interval data type in Fortran90 based on two double-precision real Fortran storage units.
Interval methods for fixed-point problems
Interval analysis is applied to the fixed-point problem x=ϕ(x) for continuous ϕ:S→S, where the space S is constructed from Cartesian products of the set R of real numbers, with componentwise…
Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition
TLDR
This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity.
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