Differentiation of interval functions
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- by Gunnar Schröder PDF
- Proc. Amer. Math. Soc. 36 (1972), 485-490 Request permission
Abstract:
This paper is concerned with differentiation of interval functions appearing in interval analysis. Two definitions of a derivative are given; the first one uses an isometric restricted imbedding of the quasilinear space of intervals on the real line R, and the other definition is independent of that imbedding. Properties of those two concepts are investigated.References
- N. Apostolatos and U. Kulisch, Grundlagen einer Maschinenintervallarithmetik, Computing (Arch. Elektron. Rechnen) 2 (1967), 89–104 (German, with English summary). MR 239720, DOI 10.1007/bf02239180
- H. T. Banks and Marc Q. Jacobs, A differential calculus for multifunctions, J. Math. Anal. Appl. 29 (1970), 246–272. MR 265937, DOI 10.1016/0022-247X(70)90078-8
- Eldon Hansen, Interval arithmetic in matrix computations. I, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 308–320. MR 187381 F. Krückeberg, Numerische Intervallrechnung und deren Anwendung, Bonn, 1966.
- O. Mayer, Algebraische und metrische Strukturen in der Intervallrechnung und einige Anwendungen, Computing (Arch. Elektron. Rechnen) 5 (1970), 144–162 (German, with English summary). MR 277134, DOI 10.1007/bf02235804
- Ramon E. Moore, Interval analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR 0231516
- Karl Nickel, Über die Notwendigkeit einer Fehlerschranken-Arithmetik für Rechenautomaten, Numer. Math. 9 (1966), 69–79 (German). MR 205507, DOI 10.1007/BF02165231
- Hans Rådström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165–169. MR 45938, DOI 10.1090/S0002-9939-1952-0045938-2
- H. Ratschek, Die binären Systeme der Intervallarithmetik, Computing (Arch. Elektron. Rechnen) 6 (1970), 295–308 (German, with English summary). MR 292332, DOI 10.1007/bf02238814
- H. Ratschek and G. Schröder, Über die Ableitung von intervallwertigen Funktionen, Computing (Arch. Elektron. Rechnen) 7 (1971), 172–187 (German, with English summary). MR 293849, DOI 10.1007/bf02242344 —, Über den quasilinearen Raum (to appear).
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 485-490
- MSC: Primary 65D99; Secondary 46N05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0311085-8
- MathSciNet review: 0311085