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Applications of Interval Computations

  • R. Baker Kearfott
  • Vladik Kreinovich

Part of the Applied Optimization book series (APOP, volume 3)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. R. Baker Kearfott, Vladik Kreinovich
    Pages 1-22
  3. Götz Alefeld, Vladik Kreinovich, Günter Mayer
    Pages 61-79
  4. Sevgui Hadjihassan, Eric Walter, Luc Pronzato
    Pages 91-131
  5. Charles L. Fefferman, Luis A. Seco
    Pages 145-167
  6. Eero Hyvönen, Stefano De Pascale
    Pages 169-209
  7. Luis Mateus Rocha, Vladik Kreinovich, R. Baker Kearfott
    Pages 337-380
  8. Michael J. Schulte, Earl E. Swartzlander Jr.
    Pages 381-404
  9. Back Matter
    Pages 417-427

About this book

Introduction

Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc­ cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli­ cations of numerical methods with automatic result verification, that were pre­ sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.

Keywords

algorithms applied mathematics fuzzy fuzzy set fuzzy sets global optimization mathematics mechanics numerical method optimization probability probability distribution quantum mechanics uncertainty verification

Editors and affiliations

  • R. Baker Kearfott
    • 1
  • Vladik Kreinovich
    • 2
  1. 1.University of Southwestern LouisianaUSA
  2. 2.University of Texas at El PasoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-3440-8
  • Copyright Information Springer-Verlag US 1996
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-3442-2
  • Online ISBN 978-1-4613-3440-8
  • Series Print ISSN 1384-6485
  • Buy this book on publisher's site
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