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Addendum to "on recurrences converging to the wrong limit in finite precision and some new examples"
Publikationstyp
Journal Article
Date Issued
2020
Sprache
English
Author(s)
Institut
TORE-URI
Volume
52
Start Page
571
End Page
575
Citation
Electronic Transactions on Numerical Analysis (52): 571-575 (2020)
Publisher DOI
Scopus ID
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.
Subjects
Bfloat
Double precision (binary64)
Exactly representable data
Half precision (binary16)
IEEE-754
Recurrences
Rounding errors
Single precision (binary32)
DDC Class
004: Informatik
510: Mathematik