I am trying to understand what is the difference between 'rate of convergence' and 'order of convergence'. Does anyone know an intuitive explanation of the difference between them?
For example, say I have the sequence defined by $(1 + 1/n^2)$, $n>=1$
So it looks like $2, 1\frac{1}{4}, 1 \frac{1}{9}, 1 \frac{1}{16},...$
And has a limit of $1$ as n approaches infinity. So what is the rate of convergence and order of convergence for this example?
And how does that sequence tie in with the convergence equation (Wikipedia - Convergence speed for iterative methods) -
$$\lim_{k\to\infty} \frac{|x_{k+1} - L|}{|x_k - L|^q} = μ | μ > 0$$