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On computing the range of a rational function of n variables over a bounded region. (English) Zbl 0345.65024

MSC:
65H10 Numerical computation of solutions to systems of equations
65G50 Roundoff error
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[1] Dussel, R.: Einschließung des Minimalpunktes einer streng konvexen Funktion auf einemn-dimensionalen Quader. Interner Bericht Nr. 72/2, Universität Karlsruhe, Institut für Praktische Mathematik, 1972. (See also: Dussel, R., in: Proceedings of a Symposium on interval mathematics. Sprincer lecture note series in Computer Sciences, 1975).
[2] Dussel, Schmitt: Die Berechnung von Schranken für den Wertebereich eines Polynoms in einem Intervall. Computing6, 35–60 (1970). · Zbl 0212.17102
[3] Hansen, E.: Interval arithmetic in matrix computations, Part I. SIAM J. Numer. Anal.2, 308 to 320 (1965). · Zbl 0135.37303
[4] Hansen, E., Smith, R.: Interval arithmetic in matrix computations, Part II. SIAM J. Numer. Anal.4, 1–9 (1967). · Zbl 0209.46601
[5] Hansen, R.: On the solution of linear algebraic equations with interval coefficients. Linear Algebra and Appl.2, 153–165 (1969). · Zbl 0185.40201
[6] Hansen, E.: The centered form. Topics in Interval Analysis (Hansen, E., ed.), pp. 102–106. Oxford U. Press 1969a.
[7] Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing4, 181–201 (1969). · Zbl 0187.10001
[8] Moore, R. E.: Interval arithmetic and automatic error analysis in digital computing. Applied Mathematics and Statistics Lab. Report 25, Stanford University (1962).
[9] Moore, R. E.: Interval Analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966. · Zbl 0176.13301
[10] Nickel, K.: On the Newton method in interval analysis. MRC Tech. Rept. No. 1136, University of Wisconsin, Madison (1971). · Zbl 0228.76060
[11] Skelboe, S.: Computation of rational interval functions. BIT, Bind 14, Hefte Nr. 1, 87–95 (1974). · Zbl 0274.65015
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