Question

xs 2x2 Use the MAT AB code for Newton-Raphson method to find a root of he function table. x 6x 4 0 with he nitial gues& xo 3.0. Perfonn the computations until relative error is less than 2%. You are required to fill the followi Iteration! 뵈 | f(x) | f(x) | Em(%) 1. Continue the computation of the previous question until percentage approximate relative error is less 2. Repeat computation uing theial guess o1.0

Answer 1

clc
clear

f = @(x) x^3-2*x^2-6*x+4; % function f(x)
fp = @(x) 3*x^2-4*x-6; %fp = drivative of f(x)

x0 = 3; %initial guess
tol = 2; %percent tolerance
%tol = 0.2; %results table 2

%{
known solutions
x =
3.4142
-2.0000
0.5858
%}

x_exact = 3.4142; % picking closest root to initial guess

i = 0;
xi = x0;

maxit = 1000; % set to avoid infinite iterations

tolerance_achieved = false;

fprintf('\n For %0.2f %% tolerance:\n\n',tol)

fprintf('iter\t\t\tx\t\t\t\t\tf(Xi)\t\t\t\tf''(Xi)\t\t\t\te(%%) \n')

while i<maxit && ~tolerance_achieved

relative_err_percent = (abs(x_exact-xi)/x_exact)*100;

fprintf('%d \t\t\t %0.4f \t\t\t\t %0.4f \t\t\t %0.4f \t\t\t %0.4f \n',i,xi,f(xi),fp(xi),relative_err_percent)

if relative_err_percent>tol
Xi = xi - (f(xi)/fp(xi));
xi = Xi;
i = i+1;
else
tolerance_achieved = true;
end

end

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