# Thread: Numerical Analysis

1. ## Numerical Analysis

I need a way to approach this problem. I saw this problem in chapter 3, section 3.4 of numerical analysis. I appreciate any help on any idea that may help me start out with this problem.

Show that the following method has third order convergence for computing R1/2

Xn+1= Xn(X2n+3R)/(3X2n+R)

Thank you.

2. ## Re: Numerical Analysis

First, what does "third order convergence" mean? What is the precise definition?

3. ## Re: Numerical Analysis

Originally Posted by Yeison

Show that the following method has third order convergence for computing R1/2

Xn+1= Xn(X2n+3R)/(3X2n+R)
What book is that from?

This iteration scheme is given by $x_{n+1}=g(x_n)$, where $g(x)=\frac{x(x^2+3R)}{3x^2+R}, x\geq 0$

The order of convergence is determined by the number of derivatives of $g$ that vanish at $x=R$.