Journal
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
Volume 52, Issue -, Pages 571-575Publisher
KENT STATE UNIVERSITY
DOI: 10.1553/etna_vol52s571
Keywords
recurrences; rounding errors; IEEE-754; exactly representable data; bfloat; half precision (binary16); single precision (binary32); double precision (binary64)
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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.
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