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International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics

SCAN 2015: Scientific Computing, Computer Arithmetic, and Validated Numerics pp 148–167Cite as

Reserve of Characteristic Inclusion as Recognizing Functional for Interval Linear Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9553))

Abstract

The paper considers the interval linear inclusion \({\varvec{C}}x\subseteq {\varvec{d}}\) in the Kaucher interval arithmetic. We introduce a quantitative measure of its fulfillment, called “reserve”, and investigate its properties and application. We show that the reserve proves useful in the study of AE-solutions and quantifier solutions to interval linear problems. In particular, using the reserve can help to recognize position of a point with respect to the solution set, emptiness of the solution set and of its interior, etc.

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Authors and Affiliations

  1. Institute of Computational Technologies, 6, Lavrentiev ave., Novosibirsk, Russia

    Irene A. Sharaya & Sergey P. Shary

Authors
  1. Irene A. Sharaya
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  2. Sergey P. Shary
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Correspondence to Sergey P. Shary .

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Editors and Affiliations

  1. Institute of Computer Science, University of Würzburg, Würzburg, Germany

    Marco Nehmeier

  2. Universität Würzburg, Würzburg, Germany

    Jürgen Wolff von Gudenberg

  3. Department of Mathematics, Uppsala University, Uppsala, Sweden

    Warwick Tucker

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Sharaya, I.A., Shary, S.P. (2016). Reserve of Characteristic Inclusion as Recognizing Functional for Interval Linear Systems. In: Nehmeier, M., Wolff von Gudenberg, J., Tucker, W. (eds) Scientific Computing, Computer Arithmetic, and Validated Numerics. SCAN 2015. Lecture Notes in Computer Science(), vol 9553. Springer, Cham. https://doi.org/10.1007/978-3-319-31769-4_13

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  • DOI: https://doi.org/10.1007/978-3-319-31769-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31768-7

  • Online ISBN: 978-3-319-31769-4

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