(1) Implement Newton\'s method, including a damping factor A. Your code should c

Question

(1) Implement Newton's method, including a damping factor A. Your code should contain a function newton(f, df, ??, 1ambda, tol), f s the function f(x) for which we want to determine a root, df is the derivative function f'(), pO is an initial guess, 1ambda is the damping parameter, and tol is the error tolerance. Your function should terminate, covering the following scenarios . The procedure converges: Stop when lpn+ Pnl tol (i.e. when the method does not improve the approximations by much. return the approximation Pn The procedure does not converge: Either p, -0, or still pntl - Pnl > tol after a large number of steps (specify this yourself, e.g. 1000). return NaN

Explanation / Answer

x = initial value // initial guess

  h = func(x)/ df(x); //value y which we will update current root

i = 0; // number of iterations

while(abs(h) > tolerance & i<=maxiter)

h = func(x)/ df(x);

x = x - h;

resarray = [resarray, x];

i=i+1;

end

Matlab code:

create a file named newton.m and paste given code into it!

function [xroot, resarray] = newton(func,df,xo,tol,maxiter)

resarray = [];

x=xo;

h = (func(x))/ (df(x));

i = 1;

while(abs(h) > tol & i<=maxiter)

h = func(x)/ df(x);

x = x - h;

resarray = [resarray, x];

i=i+1;

end

xroot = x;

end

Sample Output:

>> f = @(x) (x^2 - 4)

>> df = @(x) (2*x - 4)

>> [r,resarray] = newton(f,df,1,0.001,10)

r = -1.9971
resarray = -0.50000 -1.25000 -1.62500 -1.81250 -1.90625 -1.95312 -1.97656 -1.98828 -1.99414 -1.99707

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