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Parametric Interval Algebraic Systems

  • Book
  • © 2018

Overview

Authors:
  1. Iwona Skalna

    1. Department of Applied Computer Science, Faculty of Management, AGH University of Science and Technology, Kraków, Poland

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  • Provides a comprehensive overview of the theory related to the problem of solving parametric interval linear systems and investigates the basic properties of parametric interval matrices
  • Presents a framework for solving a general class of linear systems with coefficients being continuous functions of parameters varying within prescribed intervals
  • Includes new algorithms delivering sharp rigorous bounds for the solutions of such systems

Part of the book series: Studies in Computational Intelligence (SCI, volume 766)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxiv
    Download chapter PDF

  2. Interval Arithmetic

    • Iwona Skalna
    Pages 1-24

  3. Alternative Arithmetic

    • Iwona Skalna
    Pages 25-50

  4. Interval and Parametric Interval Matrices

    • Iwona Skalna
    Pages 51-83

  5. Linear Systems

    • Iwona Skalna
    Pages 85-98

  6. Methods for Solving Parametric Interval Linear Systems

    • Iwona Skalna
    Pages 99-163

  7. Parametric Interval Linear Programming Problem

    • Iwona Skalna
    Pages 165-172

  8. Back Matter

    Pages 173-191
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Keywords

About this book

This self-contained book presents a framework for solving a general class of linear systems with coefficients being continuous functions of parameters varying within prescribed intervals. It also provides a comprehensive overview of the theory related to solving parametric interval linear systems and the basic properties of parametric interval matrices. In particular, it develops several new algorithms delivering sharp rigorous bounds for the solutions of such systems with full mathematical rigor. The framework employs the arithmetic of revised affine forms that enables the readers to handle dependent data. The book is intended not only for researchers interested in developing rigorous methods of numerical linear algebra, but also for engineers dealing with problems involving uncertain data. The theory discussed is also useful in various other fields of numerical analysis, in computer graphics, economics, computational geometry, computer-aided design, computer-assisted proofs, computergraphics, control theory, solving constraint satisfaction problems, and global optimization.

Authors and Affiliations

  • Department of Applied Computer Science, Faculty of Management, AGH University of Science and Technology, Kraków, Poland

    Iwona Skalna

Bibliographic Information

  • Book Title: Parametric Interval Algebraic Systems

  • Authors: Iwona Skalna

  • Series Title: Studies in Computational Intelligence

  • DOI: https://doi.org/10.1007/978-3-319-75187-0

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG 2018

  • Hardcover ISBN: 978-3-319-75186-3Published: 19 February 2018

  • Softcover ISBN: 978-3-319-89287-0Published: 07 June 2019

  • eBook ISBN: 978-3-319-75187-0Published: 09 February 2018

  • Series ISSN: 1860-949X

  • Series E-ISSN: 1860-9503

  • Edition Number: 1

  • Number of Pages: XXIV, 191

  • Number of Illustrations: 26 b/w illustrations

  • Topics: Computational Intelligence, Systems Theory, Control, Artificial Intelligence

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