Addendum to "on recurrences converging to the wrong limit in finite precision and some new examples"

Link:
Autor/in:
Verlag/Körperschaft:
Hamburg University of Technology
Erscheinungsjahr:
2020
Medientyp:
Text
Schlagworte:
  • Bfloat
  • Double precision (binary64)
  • Exactly representable data
  • Half precision (binary16)
  • IEEE-754
  • Recurrences
  • Rounding errors
  • Single precision (binary32)
  • 004: Informatik
  • 510: Mathematik
Beschreibung:
  • In a recent paper [Electron. Trans. Numer. Anal, 52 (2020), pp. 358-369], we analyzed Muller's famous recurrence, where, for particular initial values, the iteration over real numbers converges to a repellent fixed point, whereas finite precision arithmetic produces a different result, the attracting fixed point. We gave necessary and sufficient conditions for such recurrences to produce only nonzero iterates. In the above-mentioned paper, an example was given where only finitely many terms of the recurrence over R are well defined, but floating-point evaluation indicates convergence to the attracting fixed point. The input data of that example, however, are not representable in binary floating-point, and the question was posed whether such examples exist with binary representable data. This note answers that question in the affirmative.
Beziehungen:
DOI 10.1553/ETNA_VOL52S571
Quellsystem:
TUHH Open Research

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Quelldatensatz
oai:tore.tuhh.de:11420/8157