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