Numerical Methods and Optimization

Numbers and Errors 47

0, 1,...,n} of n +1 values instead of X. This way we are approximating

the original problem by the problem of finding the smallest among the n +1

numbers in X

n

. Suppose that this smallest number in X

n

equals

ˆ

f =4/9,

and the exact minimum of X is f

∗

=1/12 (see Figure 2.2). Then |f

∗

−

ˆ

f| =

|1/12−4/9| =13/36 is the absolute truncation error of the considered method.

Definition 2.5 (Round-off Error) The error caused by the approxi-

mation of a numerical value with a value represented by fewer digits is

called the round-off error.

Example 2.13 Assume that we want to write our answer

˘

f to the problem in

the previous example as a five-digit de ...