Question

Please help me fix this halleyroot funtion , in matlab

function [x, er, n] = Halleyroot(fun,x1,maxtol,maxitr)
if (nargin < 5), maxitr = 25; end
if (nargin < 4), maxtol = 1e-4; end
k = 0;
er = 1;
x = x1;
funder= derivative(fun);
while er >= maxtol && k < maxitr
k = k+1; % increment the iteration number
xold = x;
x = xold-fun(xold)/funder(xold);
er = abs((x-xold)/x);
fprintf('iter = %i\t x = %f\t f(x) = %f\t er = %f \n',k,x,fun(x),er);
end
n = k; % the number of iterations performed
end

.-------------------------------------------------------------- mistake was pointed out down below

er 1 x xl funder derivative (fun) while er >= maxtol && k < maxitr k k+1; %increment the iteration number xold x x = xold-fun (xold) /fund.r (xold); er abs (x-xold) /x); fprintf(iter it this is not the algorit hm of |Halley met hod x, fun (x),er); end n k; % the number of end

Answer 1

MATLAB Function

function Halleyroot(f,x1,maxtol,error)
i = 1;
dx = diff(f); %first and second derivatives of f(x)
ddx = diff(dx);
while i <= maxtol
p = x1 - (f(x1)/dx(x1))*(1 - (f(x1)*ddx(x1)/dx(x1)^2))^(-1); %Implementation og Halleys Methof (i.e. g(x)).
  
if (abs(p - x1)/abs(p)) < error %stopping criterion when difference between iterations is below tolerance
fprintf('Solution is %f \n', double(p))
return
end

i = i + 1;
x1 = p; %update p0
end

fprintf('Solution did not coverge within %d iterations at a required precision of %d \n', maxtol, error) %error for non-convergence within N iterations

end

MATLAB script to call function

clc
clear
close
syms x
f(x)= x^2 - 6;
x1 = 1;
maxtol = 100; %maximum number of iterations
error = 0.00000001;
Halleyroot(f,x1,maxtol,error)

Result

Solution is 2.449490