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Optimal computation of the Bernstein algorithm for the bound of an interval polynomial. (English) Zbl 0475.65007


MSC:

65D15 Algorithms for approximation of functions
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
65G30 Interval and finite arithmetic
41A10 Approximation by polynomials
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References:

[1] Alefeld, G., Herzberger, J.: Einführung in die Intervallrechnung. Mannheim: Bibliographisches Institut 1974. · Zbl 0333.65002
[2] Moore, R. E.: Interval analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966. · Zbl 0176.13301
[3] Rivlin, T.: Bounds on a polynomial. Research of NBS74B, 47–54 (1970). · Zbl 0197.34704
[4] Rokne, J.: Bounds for an interval polynomial. Computing18, 225–240 (1977). · Zbl 0365.65027 · doi:10.1007/BF02253209
[5] Rokne, J.: A note on the Bernstein algorithm for bounds for interval polynomials. Computing21, 159–170 (1979). · Zbl 0391.65001 · doi:10.1007/BF02253136
[6] Rokne, J.: Optimal computation of the Bernstein algorithm for the bound of an interval polynomial. (Freiburger Intervall-Berichte 81/4, University of Freiburg, Federal Republic of Germany.)
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