As Redes Industriais

f=@(x) 6-2*(x-cos(x)+0.1);

%f=@(x) x^2+10*x+16

fplot(f, [1 2])

grid

% The plot shows, that the solution is between x = 2 and x = 3.

a = 2;

b = 3;

n = 200000; % max number of iterations

tol = 0.0; % tolerance

fa = f(a);

fb = f(b);

if fa*fb > 0

disp('Error: The function has the same sign at points a and b.')

else

disp('Iteration a b p f(p)')

for i = 1:n

p = (a + b)/2;

toli = (b - a)/2;

fp = f(p);

fprintf('%5i %13.6f %9.6f %9.6f %10.6f\n',i,a,b,p,fp)

if fp == 0

fprintf('An exact solution x=%11.6f was found',p)

break

end

if toli < tol

break

end

if i == n

fprintf('Solution was not obtained in %i iteraticns',n)

break

end

if f(a)*fp < 0

b = p;

else

a = p;

end

end

end

% The output shows that the solution with the desired tolerance

% is obtained in the 10th iteration.