1. ## newton raphson method

given f(x)=c where c is a real valued constant f(x)=cos(x) when mod(x)<=1 and f(x)=cos(x)+(x^2-1)^2 when mod(x)>=1

for a given c show that x(n)=(-1)^n, where x(0)=1

also discuss the convergence of this approximation

i applied the newton raphson method but not getting anywhere near x(n)=(-1)^n

2. ## Re: newton raphson method

The Newton-Raphson method is a method for calculating roots of non-linear equations.
Exactly what non-linear equation are you trying to solve ?

3. ## Re: newton raphson method

f(x)=cos(x)+(x^2-1)^2 is the function

4. ## Re: newton raphson method

Fine, but what does f (x)=c and x (n)=(-1)^n have to do with it ? I'll have a look at it.

5. ## Re: newton raphson method

?? The f(x) that you give is never zero. Try again.

6. ## Re: newton raphson method

is the question wrong then

7. ## Re: newton raphson method

The question as stated in #1 didn't seem to make much sense, I would be guessing as to what was meant, and the function you give in #3 doesn't have any zeros to calculate.

8. ## Re: newton raphson method

is Newton Raphson similar to an epsilon perturbation method and maybe less accurate? you can program these into software