Machine iteration of a linear function: Local behaviour (Q804225)

The paper deals with a computer which represents numbers as multiples of a discretization step \(\delta\). For floating-point representation, this means that all numbers should be of the same order of magnitude. The local behaviour of the linear function \(f(x)=ax+(1-a)\zeta\) is studied near its fixed point \(\zeta\). In the case of truncation, the author calculates the conditions needed for spurious multiple fixed points and for period-two cycles. Neither of these two errors can be reduced with better machine precision. Important qualitative differences between the schemes of roundoff and truncation are also shown.