Michael Blank
Round-off induced instabilities and some unusual arithmetics
(25K, LaTeX)

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.