Example of Noise in Function Evaluation

Execute the m-file noise.m in MATLAB.
This script looks at a small segment of the curve f(x) = (x-1)^3 in the interval 0.99998<= x <=1.00002 for 100 evenly spaced points

We do this for the function f(x) written in two different ways

First as f(x) = (x-1)^3.
The graph of the computed values of the function appears as a smooth continuous curve
Next we plot f(x)= x^3-3x^2-3x-1

Note that the graph of f(x) does not appear to be taken from a continuous curve, but rather is a narrow "fuzzy band" of seemingly random values.
This is true of all parts of the computed curve of f(x), but it becomes evident only when you look at the curve very closely
The arithmetic in MATLAB uses IEEE double precision numbers and standard rounding and this results in noise in function evaluation
Functions f(x) on a computer should be thought of as fuzzy band of random values, with the vertical thickness of the band quite small in most cases

Note: There is a large "interval of uncertainty" around the true multiple root. This can cause problems for root finding methods