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Thread: Numerical Analysis

  1. #1
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    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.
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  2. #2
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    Re: Numerical Analysis

    First, what does "third order convergence" mean? What is the precise definition?
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    Re: Numerical Analysis

    Quote Originally Posted by Yeison View Post

    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.
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