Abstract
It is proved that (set-theoretic) interval multiplication is inverse inclusion isotone. The centered outward interval multiplication (co-multiplication) is studied in some detail with respect to inclusion isotonicity. To a system of linear interval algebraic equations we associate a system involving co-multiplication. The latter reduces to two real linear systems of the same size for the midpoint-radius coordinates of the unknown intervals. We show that under certain assumptions these real linear systems produce an inner inclusion for the tolerance solution of the original interval system.
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Markov, S. (2001). Computation of Algebraic Solutions to Interval Systems Via Systems of Coordinates. In: Krämer, W., von Gudenberg, J.W. (eds) Scientific Computing, Validated Numerics, Interval Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6484-0_9
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DOI: https://doi.org/10.1007/978-1-4757-6484-0_9
Publisher Name: Springer, Boston, MA
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