Measuring the Efficiency of Numerical Procedures

• One comparison is of the number of mathematical operations that are needed to get the answer with a given accuracy. An equation
  $f(n)=\frac{n(n+1)}{2}=\frac{n^2}{2}+\frac{n}{2}$ As $n$ gets large, the first term dominates and we say that $f(n)$ if "of order $n^2$"; $f(n)=O(n^2)$.
  $n\longrightarrow double$
  $number~of~multiplications\longrightarrow four~times$
• say $x$ values differ by $h$ (commonly used variable for such spacing). The error in the answer is proportional to the third power of $h$;
  $Error=\frac{M}{6}h^3$; the error is of the order $h^3$;$Error=O(h^3)$