Newton method , student need help.

Question

Thierry Gelinas 2015-4-10

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评论： Torsten 2023-11-22

Hi , I know there's a lot of subjects on this but I didn't find what I'm looking for... This is my problem: I have create this code and it works perfectly well :

fonc=inline('fonction');
dfonc=inline('derivée de la fonction');
x=0.8;
;xn=0;
eps=1e-6;
k=0;
fprintf('   k        x_k          f(x_k)   \n');
fprintf('%4d   %12.4e  %12.4e  \n',k, x,fonc(x));
k=k+1;
while abs(x-xn) > eps & k < 20
    xn=x;
    x=x-fonc(x)/dfonc(x);
    fprintf('%4d   %12.4e  %12.4e  \n',k, x,fonc(x));
    k=k+1;
end

In this case fonction = x^4-1.3*x^3-2.97*x^2+5.929*x-2.662 and dérivée de la fonction is 4*x^3-3.9*x^2-5.94*x+5.929

   k        x_k          f(x_k)   
       0     8.0000e-01   -7.5600e-02  
       1     9.0370e-01   -2.1963e-02  
       2     9.7064e-01   -6.4300e-03  
       3     1.0144e+00   -1.8908e-03  
       4     1.0432e+00   -5.5753e-04  
       5     1.0623e+00   -1.6467e-04  
       6     1.0749e+00   -4.8691e-05  
       7     1.0833e+00   -1.4407e-05  
       8     1.0889e+00   -4.2649e-06  
       9     1.0926e+00   -1.2629e-06  
      10     1.0951e+00   -3.7405e-07  
  ...
      29     1.1000e+00    0.0000e+00

My problem is that I have to add a new thing to the table that would be create by this fonction:

abs((xn2-xn)/(xn-x)) and I don't know how to do it... I really need help.

It should be looking like this

     k        x_k          f(x_k)     |En+1/En| 
   8.0000e-01   -7.5600e-02  0,645515911
   9.0370e-01   -2.1963e-02  0,653719749
   9.7064e-01   -6.4300e-03  0,658135283
   1.0144e+00   -1.8908e-03  0,663194444
   1.0432e+00   -5.5753e-04  0,659685864
   1.0623e+00   -1.6467e-04  ...
   1.0749e+00   -4.8691e-05  ...
   1.0833e+00   -1.4407e-05  ...
   1.0889e+00   -4.2649e-06  ...
   1.0926e+00   -1.2629e-06  ...
   1.0951e+00   -3.7405e-07  ...
   1.0967e+00   -1.1080e-07  ...

Thank you. ( by the way , english is not my native language so I'm sorry for all the mistakes I may have made. )

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Answer 1

Dendani 2023-11-22

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i need the solution of this fonction méthode of newton and secante X^2-7y+5 X^3+6x^2-xy+4

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Torsten 2023-11-22

You have a system of 2 equations in 2 unknowns.

I've never heard that the secant method is used for systems of equations.

If you don't succeed or you are not keen on programming Newton's method on your own, I suggest a google search " MATLAB & Newton's method". There should be a lot of hits.

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