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

1. Apr 21, 2010

### ruby_duby

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$$/$$ log2
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 24, 2010

### Filip Larsen

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