Question

Starting from mynewton write a function program mysymnewton that takes as its input a symbolic function f and the ordinary variables x0 and n. Let the program take the symbolic derivative f ′ , and then use subs to proceed with Newton’s method. Test it on f(x) = x 3 − 4 starting with x0 = 2. Turn in the program and a brief summary of the results

Answer 1

code for matlab is
syms x
f=@(x) x^3-4;
f'=diff(f(x))
h=@(y) subs(f',y)

code for mathematica

f[x_]:=x^3-4

F'[X]                     (*THEN PRESS SHIFT AND ENTER*)

(TO GET THE VALUE FOR XO=2)

F'[2]                (*THEN PRESS SHIFT AND ENTER*)

AND SAVE PROGRAME aS mysymnewton

function [ x, ex ] = newton( f, df, x0, tol, nmax )
%
% NEWTON Newton's Method
%   Newton's method for finding successively better approximations to the 
%   zeroes of a real-valued function.
%
% Input:
%   f - input funtion
%   df - derived input function
%   x0 - inicial aproximation
%   tol - tolerance
%   nmax - maximum number of iterations
%
% Output:
%   x - aproximation to root
%   ex - error estimate
%
% Example:
%       [ x, ex ] = newton( 'x^3-4', 0, 0.5*10^-5, 10 )
%


    if nargin == 3
        tol = 1e-4;
        nmax = 1e1;
    elseif nargin == 4
        nmax = 1e1;
    elseif nargin ~= 5
        error('newton: invalid input parameters');
    end
    
    f = inline(f);
    df = inline(df);
    x(1) = x0 - (f(x0)/df(x0));
    ex(1) = abs(x(1)-x0);
    k = 2;
    while (ex(k-1) >= tol) && (k <= nmax)
        x(k) = x(k-1) - (f(x(k-1))/df(x(k-1)));
        ex(k) = abs(x(k)-x(k-1));
        k = k+1;
    end

end