Needing help with Newton Raphson method

So, I have attached my Newton Raphson script and I just want someone to double check if it is right or not. You might not see a f or fprime because they are in a different script. I'm required to make the output x1 an array that stores each new guess as it is generated and I'm having a hard time with that.

function [x1,err,iter] = newtonraphson(f,fprime,x0,tol,max_iter)

iter = 0; while (1)

    xl = x0;
    x0 = xl - f(x0)/fprime(x0);
    iter = iter + 1;
    if x0 ~= 0 
        err = abs((x0 - xl)/x0);
    end
    if err <= tol || iter >= max_iter
        break
    end

end

And then below is the driver that should use the function was created above and so display the calculated values of x1 and err for each iteration in a table formatted with fprintf. Finally, make a 1 x 3 subplot clearly showing the root-finding function and the results of each iteration. I tried everything in mind but nothing worked.

y = @(x) tanh(x.^2-9) - 3;

dy = @(x) (4.*x)./(cos(18+2.*x.^2)+1); [x1,err,iter] = newtonraphson(y,dy,3.2,0.0001,3);

Note: both scripts are written separately in two different m files. Thank you in advance

[Roger Stafford]

Your derivative of tanh(x.^2-9) is incorrect. It should be:

dy = 2*x.*sech(x.^2-9).^2 = 2*x./cosh(x.^2-9).^2

Answer 1

[Prajit T R]

Hi You can try this code:

function [xlist,err,iter] = newtonraphson(f,fprime,x0,tol,max_iter)
xlist=[x0];
iter = 0; 
x1=x0;
while (1)
  x0 = x1; %For the first iteration, it takes the value x0. For all later iterations, it takes the previous value.
  x1 = x0 - f(x0)/fprime(x0); %As per formula
  xlist(end+1)=x1; %Append the guessed value to the list 
  iter = iter + 1;
  if x0 ~= 0 
      err = abs((x0 - xl)/x0);
  end
  if err <= tol || iter >= max_iter
      break
  end
end
end

Cheers