Abstract
We show that if the conjectureP≠NP is true, then there does not exist a general polynomial-time algorithm for enclosing the solution set of a system of linear interval equations.
Zusammenfassung
Unter Annahme der VermutungP≠NP wird gezeigt, daß es keinen allgemeinen polynomialen Algorithmus gibt, der die Intervallhülle der Lösungsmenge eines Systems linearer Intervall-Gleichungen einschließt.
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Alefeld, G., Herzberger, J.: Introduction to interval computations. New York: Academic Press 1983.
Garey, M. R., Johnson, D. S.: Computers and intractability: a guide to the theory of NP-completeness. San Francisco: Freeman 1979.
Neumaier, A.: Interval methods for systems of equations. Cambridge: Cambridge University Press 1990.
Poljak, S., Rohn, J.: Checking robust nonsingularity is NP-hard. Math. Control Signals Syst.6, 1–9 (1993).
Reichmann, K.: Abbruch beim Intervall-Gauss-Algorithmus. Computing,22, 355–361 (1979).
Rohn, J., Kreinovich, V.: Computing exact componentwise bounds on solutions, of linear systems with interval data is NP-hard (to appear in SIAM J. Matr. Anal.).
Schrijver, A.: Theory of integer and linear programming. Chichester: Wiley 1986.
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Rohn, J. Enclosing solutions of linear interval equations is NP-hard. Computing 53, 365–368 (1994). https://doi.org/10.1007/BF02307386
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DOI: https://doi.org/10.1007/BF02307386