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Numerical Methods: Estimating the number of iterations the bisection method will use

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data

    Using the newton raphson method with x0=6, find the root of x2- 2 to 3dp.

    Then estimate the number of iterations the bisection method that would be required to achieve the same accuracy.

    2. Relevant equations



    3. The attempt at a solution

    I have done the first part with the newton raphson method and have found that at x5 and x6 the answer of the root of the function is 1.414

    However I am not sure how to estimate the number of iterations the bisection method will use, my guess is you use the following formula:

    make the interval [1,2] (b=2, a=1) and k= accuracy
    then

    n must be greater than or equal to: log(b-a)+klog10[tex]/[/tex] log2
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 24, 2010 #2

    Filip Larsen

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    Gold Member

    Re: Numerical Methods: Estimating the number of iterations the bisection method will

    Assuming k is the number of decimal digits in the precision (i.e. k = 6 for a precision of 10-6) and assuming you just forgot to type a parenthesis around the two log terms before diving with log 2, I get same result. If that is any help at this time :smile:
     
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