caa a22 4500 465751369 CHVBK 20180323111834.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF02262222 doi (NATIONALLICENCE)springer-10.1007/BF02262222 Alefeld G. Institut für Angewandte Mathematik, Universität Karlsruhe, Kaiserstrasse 12, D-7500, Karlsruhe 1, Federal Republic of Germany aut On the approximation of the range of values by interval expressions [Elektronische Daten] [G. Alefeld] Über die Approximation des Wertebereichs durch Intervallausdrücke If the real-valued mappingf has a representation of the formf(x)=ϕ0+ℓ(x)·h(x),x∈X where for the diameter ofh(X) the inequalityd(h(X))≤σd(X) holds and for the absolute value of ℓ(X) we have ∇ℓ(X)∇≤τd(X) n, then we introduce an interval expression forf which approximates the range of values off over the compact intervalX with ordern+1. Our result contains as a special case the theorem on higher order centered forms from [2] and a series of representations off not discussed before. Springer-Verlag, 1989 Interval arithmetic nationallicence interval expressions nationallicence Computing Springer-Verlag 44/3(1990-09-01), 273-278 0010-485X 44:3<273 1990 44 607 https://doi.org/10.1007/BF02262222 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02262222 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Alefeld G. Institut für Angewandte Mathematik, Universität Karlsruhe, Kaiserstrasse 12, D-7500, Karlsruhe 1, Federal Republic of Germany aut NATIONALLICENCE 773 0- Computing Springer-Verlag 44/3(1990-09-01), 273-278 0010-485X 44:3<273 1990 44 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer