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Linear interval equations: Computing enclosures with bounded relative or absolute overestimation is NP-hard

Интервальные системы линейных уравнений: вычисление интервальных оценок с ограниченной относительной или абсолютной погрещностью является NP-трудным

  • Mathematical Research
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Reliable Computing

Abstract

It is proved that for every δ>0, if there exists a polynomial-time algorithm for enclosing solutions of linear interval equations with relative (or absolute) overestimation better than δ, then P=NP. The result holds for the symmetric case as well.

Abstract

Доказано, что для лкхбого δ>0, еслн существуер алторнгм с-нолниомналыым временем вынолнення для локализащ ремений ннтервальной снстемы лннейных уравненщ с относнтельной (нлн абсолютной) ногрещностью, меныей δ, то P = NP. Результат снраведлнв также для случая симметричных систем.

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, 79968, El Paso, TX

    V. Kreinovich

  2. Irkutsk Computing Center, Russian Academy of Science Siberian Branch, Lermontov Str. 134, 664033, Irkutsk, Russia

    A. V. Lakeyev

Authors
  1. V. Kreinovich
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  2. A. V. Lakeyev
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Additional information

© V. Kreinovich, A. V. Lakeyev, 1996

This work was partially supported by NSF Grants No. CDA-9015006 and EEC-9322370, and by NASA Grant No. NAG 9-757. The authors are greatly thankful to Baker Kearfott, Arnold Nenmaier, and especially, to Jiri Rohn. Jiri's contribution has actually made this paper possible to an extent that we feel him practically as its co-author.

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Kreinovich, V., Lakeyev, A.V. Linear interval equations: Computing enclosures with bounded relative or absolute overestimation is NP-hard. Reliable Comput 2, 341–350 (1996). https://doi.org/10.1007/BF02389894

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  • DOI: https://doi.org/10.1007/BF02389894

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