Newton-Raphson algorithm stuck running after 4 or 5 iterations

Code:

%% initial setup
syms x real
f = x^5-2*x^3+4*x+2;
error_lim = 1e-5;
%% newton raphson
d_f = diff(f);
m = 5;
disp(m)
% iterate till root is found with certain accuracy
more off;
while true
    e = m - subs(f,m)/subs(d_f,m);
    err = abs(e-m);
    fprintf("error = %g\n", err)
    if err < error_lim
        break
    end
    m = e;
    fprintf("x_p = %g\n", m)
end
fprintf("the root newton raphson method is %g\n", e)

and the output is:

>> stat3_b

5

error = 0.972474

x_p = 4.02753

error = 0.774926

x_p = 3.2526

error = 0.620288

x_p = 2.63231

error = 0.505877

x_p = 2.12643

error = 0.439351

x_p = 1.68708

error = 0.467107

x_p = 1.21998

error = 0.968289

x_p = 0.251687

error = 0.817551

x_p = -0.565863

After 8th iterations matlab is busy, but nothing prints. It runs and gives appropriate solution of the function when initial m is set to 1 or 2 but problem arises when m is set to 3 or higher. What is wrong with the above allgorithm?

Thanks in advance.

Answer 1

[Dyuman Joshi]

Converting to numeric data type is much faster than using symbolic values

syms x real
%I have defined f to be an explicit function of x, so that you can directly input 
%the value to get the output instead of using subs()
f(x) = x^5-2*x^3+4*x+2;
error_lim = 1e-5;

%% newton raphson
%as a result, d_f is also an explicit function of x
d_f = diff(f)

d_f(x) = 

m = 5;
while true
    %conversion to double
    e = m - double(f(m)/d_f(m));
    err = abs(e-m);
    %fprintf("error = %g\n", err)
    if err < error_lim
        break
    end
    m = e;
    %fprintf("x_p = %g\n", m)
end

%Succesful completion of while loop and result is obtained
fprintf("the root newton raphson method is %g\n", e)

the root newton raphson method is -0.581803

[Mosharof Hossain]

thanks