Abstract
We give necessary and sufficient conditions for the solution set of a system of linear interval equations to be nonconvex and derive some consequences.
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References
W. Barth and E. Nuding, Optimale Lösung von Intervallgleichungssystemen, Computing 12 (1974), 117–125.
M. Fiedler and V. Pták,On matrices with non-positive off-diagonal elements and positive principal minors, Czech. Math. Journal 12 (1962), 382–400.
D. Gay,Solving interval linear equations, SIAM J. Numer. Anal. 19 (1982), 858–870.
E. Hansen,On linear algebraic equations with interval coefficients, in:Topics in Interval Analysis (E. Hansen, Ed.), Clarendon Press, Oxford 1969.
K. Nickel, Die Überschätzung des Wertebereichs einer Funktion in der Intervallrechnung mit Anwendungen auf lineare Gleichungssysteme, Computing 18 (1977), 15–36.
W. Oettli,On the solution set of a linear system with inaccurate coefficients, SIAM J. Numer. Anal. 2 (1965), 115–118.
W. Oettli and W. Prager,Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides, Numerische Mathematik 6 (1964), 405–409.
J. Rohn,Interval linear systems, Freiburger Intervall-Berichte 84/7, 33–58.
J. Rohn,Systems of linear interval equations, to appear in Lin. Alg. Appls.
G. Alefeld and J. Herzberger,Introduction to Interval Computations, Academic Press, New York 1983.
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Rohn, J. On nonconvexity of the solution set of a system of linear interval equations. BIT 30, 161–165 (1990). https://doi.org/10.1007/BF01932142
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DOI: https://doi.org/10.1007/BF01932142