Question

MATLAB Newtons Method. Use initial guess of xo. Use Matlab. x2-3x2+ 3x - 1 = 0

Answer 1

MATLAB Script:

close all
clear
clc

syms x
f = x^3 - 3*x^2 + 3*x - 1;
x0 = 0; tol = 1e-9;
newton_raphson(f, x0, tol);

function x = newton_raphson(f, x0, tol)
x = x0; xold = x0; num_iter = 0;
df = diff(f);
while true
num_iter = num_iter + 1;
x = x - subs(f,x)/subs(df,x); % Newton Update Rule
if abs(x - xold) < tol % Termination condition
break
end
xold = x;
end
fprintf('Solution: %.6f, Number of Iterations: %d, Tolerance: %e\n', x, num_iter, tol)
end

Output:

Solution: 1.000000, Number of Iterations: 50, Tolerance: 1.000000e-09