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Ralph Baker Kearfott schrieb:
P.S. Opinion: As someone with mathematical training, I would prefer
"min-max" to "inf-sup" since the min and the max exist,
because the mathematical objects to which we refer are closed
and bounded sets. However, we are definitely stuck with
"inf-sup," because that's
what practically everyone uses everywhere. In any case,
a "min" is an "inf" and a "max" is a "sup."
Best regards,
Baker
Baker:I am also not very happy about "inf-sup". An interval is denoted by an ordered pair [a, b]. The first element is the lower bound and the second is the upper bound. So would not lower bound (lb) and upper bound (ub) be better?
The intervals IR over the real numbers and IF over the floating-point numbers are both (completely) ordered sets with respect to set inclusion as an order relation. The 'tightest' enclosure of an interval A of IR in IF is just the least upper bound (the supremum of A (sup A)) in IF. A 'valid' enlosure of an interval A of IR in IF just maps A on an upper bound in IF. So we could use conventional mathematical concepts and would not have to develop a particular interval jargon.
Best regards Ulrich -- Karlsruher Institut für Technologie (KIT) Institut für Angewandte und Numerische Mathematik (IANM2) D-76128 Karlsruhe, Germany Prof. Ulrich Kulisch Telefon: +49 721 608-2680 Fax: +49 721 608-6679 E-Mail: ulrich.kulisch@xxxxxxx www.kit.edu www.math.kit.edu/ianm2/~kulisch/ KIT - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gemeinschaft