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NPHard Classes of Linear Algebraic Systems with Uncertainties
 Anatoly V. Lakeyev,
 Vladik Kreinovich
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For a system of linear equations Ax = b, the following natural questions appear:
• does this system have a solution?
• if it does, what are the possible values of a given objective function f(x1,...,xn) (e.g., of a linear function f(x) = ∑C _{ i } X _{ i }) over the system's solution set?
We show that for several classes of linear equations with uncertainty (including interval linear equations) these problems are NPhard. In particular, we show that these problems are NPhard even if we consider only systems of n+2 equations with n variables, that have integer positive coefficients and finitely many solutions.
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 Title
 NPHard Classes of Linear Algebraic Systems with Uncertainties
 Journal

Reliable Computing
Volume 3, Issue 1 , pp 5181
 Cover Date
 19970201
 DOI
 10.1023/A:1009938325229
 Print ISSN
 13853139
 Online ISSN
 15731340
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Authors

 Anatoly V. Lakeyev ^{(1)}
 Vladik Kreinovich ^{(2)}
 Author Affiliations

 1. Irkutsk Computing Center, Siberian Branch, Russian Academy of Sciences, Lermontov Str. 134, 664033, Irkutsk, Russia
 2. Department of Computer Science, University of Texas at, El Paso, El Paso, TX, 79968, USA, email