To illustrate the error analysis of the previous exercise,
approximate the
derivative of at **x = 0** with the centered difference formula and
compare with the
exact value of the derivative using step sizes ranging from to
.
Use ** xmgr** to produce a log--log plot of the error.
On your computer, what appears to be a choice of **h** that
minimizes the sum of the rounding/precision error and the truncation error for
this calculation?
Show how your results change when you use 32 bit, 64 bit, and 128 bit precision
in your floating point calculations.