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Outer Bounds for the Parametric Controllable Solution Set with Linear Shape

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Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2015)

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

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Abstract

We consider linear algebraic equations, where the elements of the matrix and of the right-hand side vector are linear functions of interval parameters, and their parametric AE-solution sets, which are defined by universal and existential quantifiers for the parameters. We present how some sufficient conditions for a parametric AE-solution set to have linear boundary can be exploited for obtaining sharp outer bounds of that parametric AE-solution set. For a parametric controllable solution set having linear boundary we present a numerical method for outer interval enclosure of the solution set. The new method has better properties than some other methods available so far.

This work is dedicated to the memory of Prof. Dr. Walter Krämer (1952-2014), Univ. of Wuppertal, Germany.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Block 8, 1113, Sofia, Bulgaria

    Evgenija D. Popova

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  1. Evgenija D. Popova
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Correspondence to Evgenija D. Popova .

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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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Popova, E.D. (2016). Outer Bounds for the Parametric Controllable Solution Set with Linear Shape. 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_12

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  • DOI: https://doi.org/10.1007/978-3-319-31769-4_12

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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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