# Rate of convergence and asymptotic error constant

1. Jan 8, 2009

### azay

In the context of root finding algorithms such as secant, regula falsi, bisection, Newton's method:

In

$$\lim_{n \to \infty} \frac{|x*-x_{n+1}|}{|x*-x_{n}|^{p}} = C$$

I understand the meaning of the order p is the speed of convergence. For example, in Newton's method the order p = 2 and thus the number of correct significant digits is approximately doubled in each iteration step. But is there an intuitive meaning to be given to the asymptotic error constant C? What does this number mean? What is the difference between two methods that have the same order p, but for a different C?

2. Feb 4, 2009

### Mathman85

As I understand it, if they are of the same order, the method with a smaller C will converge faster.

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