Authors:
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)
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Front Matter
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Back Matter
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
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Informática, Matemática Aplicada y Estadística, Escola Politecnica Superior, University of Girona, Girona, Spain
Miguel A. Sainz, Remei Calm
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Enginyeria Elèctrica, Electrònica i Automàtica, Escola Politecnica Superior, University of Girona, Girona, Spain
Joaquim Armengol, Josep Vehi
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Imperial College London, London, United Kingdom
Pau Herrero
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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, Numerical Analysis