Numerical Methods with VBA Programming

  3    Errors, Series, and Uncertainty

3.1 Types of Errors

Errors in numerical analysis result because we are making approximations. If we are approximating a noninteger, we have to write it to a finite number of places: for example, we may write ¹ as 0.33 or 0.3333 or 0.333 333 333 333, but at some point we are going to stop writing 3′s and thus slightly underrepresent the exact value. The opposite occurs with 3 when eventually we round up the last 6 to a 7 and thus slightly overrepresent the quantity. These differences constitute round-off error.

On the other hand, if we are evaluating a series, we may take 1 or 5 or even 100 terms, but eventually ...