Plotting approximation error in Newton-Raphson

Hello all,

In a script I'm trying to find roots of a function by Newton-Raphson method. In each iteration I'm finding and printing the relative approximation error.

What I want is, instead of printing them I would like plot my function and my relative approximation error in each iteration.

Any help is much appreciated.

My script file:

function [r] = newton(x1)
n = 1000;
tol_error = 0.001;
r = x1;
for t=1:n
 x_plus = x1 - (my_func(x1)/my_func_diff(x1));
 approx_error(t) = abs((x_plus - x1)/(x_plus))*100;
 if (approx_error(t) < tol_error)
      display(t);
     display(approx_error(t));
     r = x_plus;
     return;
 else
     x1 = x_plus;
 end
end
end

function y = my_func_diff(x)
y = 3*(x^2) - 20*x - 43;
end
function y = my_func(x)
y = x^3 - 10*(x^2) - 43*x + 52;
end

Answer 1

[Mischa Kim]

Hidir, I assume you are using a while-loop that you execute until the relative error is smaller than some given tolerance. Something like:

 ii = 0;                  % define a loop index (= iteration number)
 while (abs(err) > tol)
   ii = ii + 1;           % increment loop index
   ...                    % do some computations
   err(ii) = ...          % compute and save relative error as vector
 end

 plot(ii,err,'rs',ii,fun) % plot error along with function value

[Hidir]

Doesn't seem to be working mate. I included my code, it might help you.

[Mischa Kim]

Here you go:

 function [r] = newton(x1)
 n = 1000;
 tol_error = 0.00001;
 r = x1;
 for t=1:n
    x_plus = x1 - (my_func(x1)/my_func_diff(x1));
    approx_error(t) = abs((x_plus - x1)/(x_plus))*100;
    fun_val(t) = my_func(x1);  % save function values as vector
    if (approx_error(t) < tol_error)
        display(t);
        display(approx_error(t));
        r = x_plus;
        break;                 % use break instead of return
    else
        x1 = x_plus;
    end
 end

 plot(1:t,approx_error,'rs-',1:t,fun_val,'bd-')
 grid
 end

[Hidir]

Works like a charm. Ty !