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Modal Interval Analysis

New Tools for Numerical Information

  • Book
  • © 2014

Overview

Authors:
  1. Miguel A. Sainz

    1. Informática, Matemática Aplicada y Estadística, Escola Politecnica Superior, University of Girona, Girona, Spain

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  2. Joaquim Armengol

    1. Enginyeria Elèctrica, Electrònica i Automàtica, Escola Politecnica Superior, University of Girona, Girona, Spain

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  3. Remei Calm

    1. Informática, Matemática Aplicada y Estadística, Escola Politecnica Superior, University of Girona, Girona, Spain

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  4. Pau Herrero

    1. Imperial College London, London, United Kingdom

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  5. Lambert Jorba

    1. Matemática Económica, Financiera y Actuarial, Facultad de Economia y Empresa, Universitat de Barcelona, Barcelona, Spain

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  6. Josep Vehi

    1. Enginyeria Elèctrica, Electrònica i Automàtica, Escola Politecnica Superior, University of Girona, Girona, Spain

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  • Develops of a new interval theory
  • Presents several sample applications
  • Includes many examples to illustrate the main results
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2091)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Intervals

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 1-16

  3. Modal Intervals

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 17-37

  4. Modal Interval Extensions

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 39-72

  5. Interpretability and Optimality

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 73-120

  6. Interval Arithmetic

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 121-141

  7. Equations and Systems

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 143-158

  8. Twins and f ∗Algorithm

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 159-183

  9. Marks

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 185-228

  10. Intervals of Marks

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 229-264

  11. Some Related Problems

    • Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 265-305

  12. Back Matter

    Pages 307-318
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Keywords

About this book

This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals through the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computations.

Authors and Affiliations

  • Informática, Matemática Aplicada y Estadística, Escola Politecnica Superior, University of Girona, Girona, Spain

    Miguel A. Sainz, Remei Calm

  • Enginyeria Elèctrica, Electrònica i Automàtica, Escola Politecnica Superior, University of Girona, Girona, Spain

    Joaquim Armengol, Josep Vehi

  • Imperial College London, London, United Kingdom

    Pau Herrero

  • Matemática Económica, Financiera y Actuarial, Facultad de Economia y Empresa, Universitat de Barcelona, Barcelona, Spain

    Lambert Jorba

Bibliographic Information

  • Book Title: Modal Interval Analysis

  • Book Subtitle: New Tools for Numerical Information

  • Authors: Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-01721-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Softcover ISBN: 978-3-319-01720-4Published: 02 December 2013

  • eBook ISBN: 978-3-319-01721-1Published: 18 November 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 316

  • Number of Illustrations: 34 b/w illustrations, 3 illustrations in colour

  • Topics: Analysis, Control and Systems Theory, Numeric Computing

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