Interval solutions for interval algebraic equations

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 pres...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 66; no. 2-3; pp. 207 - 217
Main Authors Polyak, B.T., Nazin, S.A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 29.06.2004
Subjects
Interval bounding
Interval solution
Linear interval equations
Solution set
Interval solution
Solution set
Linear interval equations
Interval bounding
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2003.11.006