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Ill take it from the top please excuse me for any misspellings.
In Numerical analysis, I have to show that a function only converges towards a solution in a certain interval.
The function is
f(x)=x/8+arctg(x)
Im using Newtons method, i.e.
xk+1 = xk - f(x)/f'(x)
And i know it will converge if I am in an interval that satisfies
|xk-xk+1| < 2xk
I then use that
f(x)/f'(x) < 2xk
giving me
1+8*arctg(x)/x
--------------- < 2
1+8/1+x^2
My problem is now how to solve this inequality, i'm trying with mathematica, but i cant make it work
Its not important how I solve it, i just need a solution, and guidelines to finding it...
Anyone up for the task?
In Numerical analysis, I have to show that a function only converges towards a solution in a certain interval.
The function is
f(x)=x/8+arctg(x)
Im using Newtons method, i.e.
xk+1 = xk - f(x)/f'(x)
And i know it will converge if I am in an interval that satisfies
|xk-xk+1| < 2xk
I then use that
f(x)/f'(x) < 2xk
giving me
1+8*arctg(x)/x
--------------- < 2
1+8/1+x^2
My problem is now how to solve this inequality, i'm trying with mathematica, but i cant make it work
Its not important how I solve it, i just need a solution, and guidelines to finding it...
Anyone up for the task?