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Interval solutions for interval algebraic equations

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  • Polyak, B.T.
  • Nazin, S.A.

Abstract

In the framework of interval uncertainty, a well-known classical problem in numerical analysis is considered, namely, to find “the best” interval solution for interval system of linear algebraic equations. This problem is known to be NP-hard and can be solved via multiple linear programming. In present paper, a simple approach is proposed for some particular models of interval uncertainty. This method gives an optimal interval solution without linear programming and is tractable for moderate-size problems. For large-scale problems an effective overbounding technique is developed.

Suggested Citation

  • Polyak, B.T. & Nazin, S.A., 2004. "Interval solutions for interval algebraic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(2), pages 207-217.
    • Handle: RePEc:eee:matcom:v:66:y:2004:i:2:p:207-217
    DOI: 10.1016/j.matcom.2003.11.006
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    References listed on IDEAS

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    1. NESTEROV, Yu., 1998. "Semidefinite relaxation and nonconvex quadratic optimization," LIDAM Reprints CORE 1362, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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