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A Comment on the Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients

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Reliable Computing

Abstract

This article is a short supplement to our previously published paper, in which we proved that each semialgebraic set can be represented as a projection of a solution set of some system of interval linear equations with dependent coefficients. The new result says that interval occurring can be chosen as narrow as wanted. The new result is proved by a simple linear transformation.

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References

  1. Alefeld, G., Kreinovich, V., and Mayer, G.: The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients, Math. Nachr. 192 (1998), pp. 23–36.

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  2. Kreinovich, V., Lakeyev, A., Rohn, J., and Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations, Kluwer Academic Publishers, Dordrecht, 1997.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Karlsruhe, D-76128, Karlsruhe, Germany

    Götz Alefeld

  2. Department of Computer Science, The University of Texas at El Paso, El Paso, TX, 79968, USA

    Vladik Kreinovich

  3. Fachbereich Mathematik, Universität Rostock, D-18051, Rostock, Germany

    Günter Mayer

  4. Computing and Information Sciences, Kansas State University, Manhattan, KS, 66506, USA

    Michael Huth

Authors
  1. Götz Alefeld
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  2. Vladik Kreinovich
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  3. Günter Mayer
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  4. Michael Huth
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Alefeld, G., Kreinovich, V., Mayer, G. et al. A Comment on the Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients. Reliable Computing 7, 275–277 (2001). https://doi.org/10.1023/A:1011455122425

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  • DOI: https://doi.org/10.1023/A:1011455122425

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