Volume 52, pp. 358-369, 2020.
On recurrences converging to the wrong limit in finite precision and some new examples
Siegfried M. Rump
Abstract
In 1989, Jean-Michel Muller gave a famous example of a 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 analyze recurrences in that spirit and remove a gap in
previous arguments in the literature, that is, the recursion must be well defined. The latter is known as the Skolem problem. We identify initial values
producing a limit equal to the repellent fixed point, show that
in every
Full Text (PDF) [596 KB], BibTeX , DOI: 10.1553/etna_vol52s358
Key words
recurrences, rounding errors, IEEE-754, different precisions, bfloat, half precision (binary16), single precision (binary32), double precision (binary64), extended precision (binary128), multiple precision, Skolem problem, Pisot sequence
AMS subject classifications
65G50, 11B37
ETNA articles which cite this article
Vol. 52 (2020), pp. 571-575 Siegfried M. Rump: Addendum to “On recurrences converging to the wrong limit in finite precision and some new examples” |