Abstract
How good an estimate can we get by applying "naive" interval computations technique to a given function f(x 1,...,x n ) over given intervals x1,...,x n ? This question was raised in several papers and conference presentations by G. Alefeld, R. Lohner, and others.
Recently, several results have been proven which show, crudely speaking, that whatever reformulation g(x 1,...,x n ) we choose, we cannot hope to get the exact range for all possible input intervals. However, a question remains: it is possible, for each sequence of input intervals, to find a reformulation which leads to exact range for this particular sequence of input intervals? If not, which enclosures can we thus get? In this paper, we show that if we allow min and max, then, for fixed input intervals, we can get an arbitrary superinterval of the actual range (including the exact range itself).
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Koshelev, M. Every Superinterval of the Function Range Can Be an Interval-Computations Enclosure. Reliable Computing 6, 219–223 (2000). https://doi.org/10.1023/A:1009977508817
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DOI: https://doi.org/10.1023/A:1009977508817