Editing Richardson extrapolation (section)

=== Notation ===
Let <math>A_0(h)</math> be an approximation of ''<math>A^*</math>''(exact value) that depends on a step size {{mvar|h}} (where <math display="inline">0 < h < 1</math>) with an [[Approximation error|error]] formula of the form 
<math display="block"> A^* = A_0(h)+a_0h^{k_0} + a_1h^{k_1} + a_2h^{k_2} + \cdots </math>
where the <math>a_i</math> are unknown constants and the <math>k_i</math> are known constants such that <math>h^{k_i} > h^{k_{i+1}}</math>. Furthermore, <math>O(h^{k_i})</math> represents the [[truncation error]] of the <math>A_i(h)</math> approximation such that <math>A^* = A_i(h)+O(h^{k_i}).</math> Similarly, in <math>A^*=A_i(h)+O(h^{k_i}),</math> the approximation <math>A_i(h)</math> is said to be an <math>O(h^{k_i})</math> approximation.

Note that by simplifying with [[Big O notation]], the following formulae are equivalent:
<math display="block"> \begin{align} 
A^* &= A_0(h) + a_0h^{k_0} + a_1h^{k_1} + a_2h^{k_2} + \cdots \\  
A^* &= A_0(h)+ a_0h^{k_0} + O(h^{k_1}) \\
A^* &= A_0(h)+O(h^{k_0}) 
\end{align} </math>