Write a function newton f fprime x0 tol that implements Newt

Write a function newton (f, fprime, x0, tol) that implements Newton\'s iteration for rootfinding on a scalar function: The first two inputs are handles to functions computing f and f\', and the third input is an initial root estimate. Continue the iteration until either is less than tol.

Solution

Reuired Matlab function is

function root=newton(f,fprime,x0,tol)
if(abs(f(x0))<=tol)
    root = x0;
    return;
else
    while(abs(f(x0))>tol)
        xnew=x0-(f(x0)/fprime(x0));
        x0=xnew;
    end
    root = x0;
end
end

Example run:

Smaple Input

f=@(x) cos(x)-3*x+1

fprime=@(x) -sin(x)-3

tol=10^-3

x0=1

newton(f,fprime,x0,tol)

Sample Output:

ans =    0.6071