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Interval Linear Algebra and Computational Complexity

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Applied and Computational Matrix Analysis (MAT-TRIAD 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 192))

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Abstract

This work connects two mathematical fields – computational complexity and interval linear algebra . It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system , deciding solvability of a linear system , computing inverse matrix , eigenvalues , checking positive (semi)definiteness or stability . We discuss these problems and relations between them from the view of computational complexity . Many problems in interval linear algebra are intractable, hence we emphasize subclasses of these problems that are easily solvable or decidable. The aim of this work is to provide a basic insight into this field and to provide materials for further reading and research.

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Notes

  1. 1.

    In computer science it is sometimes emphasized that the functions are defined for each input, or total for short. This is to distinguish them from partially defined functions which are also studied in this area, namely within logic and recursion theory.

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Acknowledgements

J. Horáček and M. Hladík were supported by GAČR grant P402/13-10660S. M. Černý was supported by the GAČR grant 16-00408S.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00, Prague, Czech Republic

    Jaroslav Horáček & Milan Hladík

  2. Faculty of Computer Science and Statistics, University of Economics, nám. W. Churchilla 4, 13067, Prague, Czech Republic

    Michal Černý

Authors
  1. Jaroslav Horáček
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  2. Milan Hladík
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  3. Michal Černý
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Corresponding author

Correspondence to Jaroslav Horáček .

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Editors and Affiliations

  1. Department of Mathematics, University of Coimbra, Coimbra, Portugal

    Natália Bebiano

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Horáček, J., Hladík, M., Černý, M. (2017). Interval Linear Algebra and Computational Complexity. In: Bebiano, N. (eds) Applied and Computational Matrix Analysis. MAT-TRIAD 2015. Springer Proceedings in Mathematics & Statistics, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-49984-0_3

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