# Thread: Newton Raphson Method ,Help needed

1. ## Newton Raphson Method ,Help needed

Hi, i have been asked to create a function newton.m which takes as input f(x),f'(x) and root esitmate x0 and throws out the true root of f(x) using the newton raphson method.
after i have created my file,i have to find the root of the 75^(1/3) which is the cuberoot of 75

here is where i have reached thus far:

dont know whats going wrong.

function [root,x] = newton(a,tol)
f(a)=75^(1/3)
fp(a)=0
test = abs(f(a));
i = 0;
x(i+1) = a;
%while test > tol
for i=1:30
a = a - f(a)/fp(a);
test = abs(f(a));
i = i+1;
x(i+2) = a;
end
i

root = a;

can anyone tell me wherei m going wrong,here is what i get when i try to run the file:

>> newton(1,1e-6)

f =

4.2172

fp =

0

??? Attempted to access f(-Inf); index must be a positive integer or logical.

Error in ==> newton at 11
test = abs(f(a));

2. Originally Posted by mithilesh
Hi, i have been asked to create a function newton.m which takes as input f(x),f'(x) and root esitmate x0 and throws out the true root of f(x) using the newton raphson method.
after i have created my file,i have to find the root of the 75^(1/3) which is the cuberoot of 75

here is where i have reached thus far:

dont know whats going wrong.

function [root,x] = newton(a,tol)
f(a)=75^(1/3)
fp(a)=0
test = abs(f(a));
i = 0;
x(i+1) = a;
%while test > tol
for i=1:30
a = a - f(a)/fp(a);
test = abs(f(a));
i = i+1;
x(i+2) = a;
end
i

root = a;

can anyone tell me wherei m going wrong,here is what i get when i try to run the file:

>> newton(1,1e-6)

f =

4.2172

fp =

0

??? Attempted to access f(-Inf); index must be a positive integer or logical.

Error in ==> newton at 11
test = abs(f(a));
First you are looking for the cube root of 75, so we want the root of the equation:

$f(x)=x^3-75$

and

$f'(x)=5x^2$

Then the NR ittereation is:

$x_{new}=x_{old}-\frac{f(x_{old})}{f'(x_{old})}$

so we start with functions defining $f$ and $f'$

Code:
function rv=ffcubert(x)
rv=x^3-75;
Code:
function rv=ffdcubert(x)
rv=3*x^2;
Then the NR itteration:

Code:
function rt=NRroot(f,fdot,x0,tol)
%================================================
% f the function we wish to find the root of (function handle)
% fdot the derivative of f
% x0 initial guess at the root
% tol stopping tolerance
%================================================
xx=x0;
err=1e6;
while err>tol
fxx=feval(f,xx);
fxxdot=feval(fdot,xx);
xnew=xx-fxx/fxxdot;
err=abs(xnew-xx);
xx=xnew;
end
rt=xx;
Then the call command:

Code:
 >> NRroot(@ffcubert,@ffdcubert,1,0.01)

ans=

4.2172

>>
RonL

3. Thank you,captain black. and also i had one more request,if u can look at the problem in very urgent section.
i m having a problem plotting the root,
any sort of help will be appreciated

thank you again.