Abstract
Interval slopes are known to provide sharper enclosures for the range of factorable functions in comparison to interval derivatives. Presently, only the rational part of the functions is, however, treated by way of interval slopes while interval derivatives are used for the irrational components.
In this paper, it is suggested to use, whenever appropriate, first- or second-order slopes for the irrational components of the factorable functions also. Theoretical considerations as well as illustrative examples show that the new approach leads to enclosures for the range that are narrower in comparison with those obtained by the traditional scheme.
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Kolev, L.V. Use of Interval Slopes for the Irrational Part of Factorable Functions. Reliable Computing 3, 83–93 (1997). https://doi.org/10.1023/A:1009902813842
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DOI: https://doi.org/10.1023/A:1009902813842