Abstract
It is proved that each element of the solution set of a system of interval linear equations is asolution of a system Ax = b in certain “normal form”: in each equation of Ax = b every coefficient, with exception of at most one, is equal either to the lower or to the upper bound on it. Even more, the distribution of the lower and upper bounds in A follows a specific pattern.
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References
Oettli, W. and Prager, W.: Compatibility of Approximate Solution of Linear Equations with Given Error Bounds for Coefficients and Right-Hand Sides, Numerische Mathematik 6 (1964), pp. 405–409.
Rohn, J.: Interval Linear Systems, Freiburger Intervall-Berichte 84 (7), Albert-Ludwig University, Freiburg, 1984.
Rohn, J.: Miscellaneous Results on Linear Interval Systems, Freiburger Intervall-Berichte 85 (9), Albert-Ludwig University, Freiburg, 1985.
Rohn, J.: Systems of Linear Interval Equations, Linear Algebra and Its Applications 126 (1989), pp. 39–78.
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Rohn, J. A Normal Form Supplement to the Oettli-Prager Theorem. Reliable Comput 11, 35–39 (2005). https://doi.org/10.1007/s11155-005-5941-9
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DOI: https://doi.org/10.1007/s11155-005-5941-9