Matlab shows results as a formula when i need a numeric value

I am trying to write modified newton formula in matlab, but the matlab shows results x form, not numeric. here is the code.

clc
format long g
syms x;
fun = input ('Enter the function f(x)= : ');
f=inline(fun);
z=diff(f(x));
f1=inline(z);
z1=diff(f1(x));
f2=inline(z1);
u1=[f(x)/f1(x)];
u2={1-[(f(x)*f2(x))/(f1(x)^2)]};
x0=input('enter the first guess x0=: ');
for i=0:6
    xn=x;
    x=xn-[u1/u2];
end
i

and the results are,

I am trying to write modified newton formula in matlab, but the matlab shows results x form, not numeric. here is the code.

clc format long g syms x; fun = input ('Enter the function f(x)= : ','s'); f=inline(fun); z=diff(f(x)); f1=inline(z); z1=diff(f1(x)); f2=inline(z1); u1=f(x)/f1(x); u2=1-[(f(x)*f2(x))/(f1(x)^2)]; x0=input('enter the first guess x0=: '); for i=0:6 xn=x x=xn-[u1/u2]; if x==xn break end end and here are the results;

Enter the function f(x)= : x^2-2 enter the first guess x0=: 1

xn = x

xn = x + (x^2 - 2)/(2*x*((2*x^2 - 4)/(4*x^2) - 1))

xn = x + (x^2 - 2)/(x*((2*x^2 - 4)/(4*x^2) - 1))

xn = x + (3*(x^2 - 2))/(2*x*((2*x^2 - 4)/(4*x^2) - 1))

xn = x + (2*(x^2 - 2))/(x*((2*x^2 - 4)/(4*x^2) - 1))

xn = x + (5*(x^2 - 2))/(2*x*((2*x^2 - 4)/(4*x^2) - 1))

xn = x + (3*(x^2 - 2))/(x*((2*x^2 - 4)/(4*x^2) - 1))

how can i fix that? thanks.

Answer 1

[Christiaan]

Dear Hakan,

The Funktion inline will be removed in a future release of Matlab Inline (Mathworks) . Therefore an another way to use the newthon ralphson technique is by this code:

clc;clear all;close all; syms x; fun = input ('Enter the function f(x)= : ','s'); fun = sym(fun); derfun = diff(fun,x); x0=input('enter the first guess x0=: ');

for i=1:10 if i==1 x_old = x0; else x_old = x_new; end

      fx_old = subs(fun,x,x_old);
      dfdx_old = subs(derfun,x,x_old);
      x_new = x_old-(fx_old/dfdx_old)
      x_new = vpa(x_new,6) ;
      if x_old==x_new 
          break 
      end       
  end

Good Luck! Christiaan

[hakan Karatay]

Dear Christiaan, thanks for the answer. But i try to code "modified newton formula" I attached the formula on my comment. there is a little difference in this method.

[Christiaan]

Hello Hakan,

I modified the code for you:

clc;clear all;close all; 
syms x; 
fun = input ('Enter the function f(x)= : ','s'); 
fun = sym(fun); 
derfun = diff(fun,x); 
derfun2 = diff(derfun,x); 
x0=input('enter the first guess x0=: ');

for i=1:30 
    if i==1 
        x_old = x0; 
    else
        x_old = x_new; 
    end
  fx_old = subs(fun,x,x_old);
  dfdx_old = subs(derfun,x,x_old);
  d2fdx2_old = subs(derfun2,x,x_old);
  u_1 = fx_old/dfdx_old;
  u_2 = 1-(fx_old*d2fdx2_old)/(dfdx_old*dfdx_old);

    x_new = x_old-(u_1/u_2)
    x_new = vpa(x_new,6) ;

    if x_old==x_new 
        break 
    end       
    end

Kind regards, Christiaan