Newton-Raphson & Bisection Methods to Find x2- 2 Root

[ruby_duby]

Homework Statement

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.

Homework Equations

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

 

[Filip Larsen]

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