95-47 Michael Blank

Round-off induced instabilities and some unusual arithmetics (25K, LaTeX) Feb 14, 95

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Abstract. We consider some unusual phenomena that appear in long consecutive calculations due to a new sort of round-off errors of Pentium floating point division bug type. Mathematical model of these round-off errors is proposed and new phenomena in numerical simulations of dynamical systems (differential equations) and other numerical procedures are discussed. It is shown also that these new phenomena could appear not only with Pentium floating point division bugs, but in a more general situation, when one tooks into account round-off errors on the each elementary step of calculations, rather than on the final step only. P.S. Figure 3 is available upon request in PS-format.

Files: 95-47.tex