how to solve newton method ?

hello,

what is wrong with my code .. I get Error in fevel .

fun =inline( '[x(1)^2+ x(2)^2 + x(3)^2 -1 ;
                 x(1)^2 + x(3)^2-0.25 ;
                 x(1)^2+ x(2)^2 + 4*x(3) ]');
J =  inline ('[2*x(1), 2*x(2), 2*x(3);
               2*x(1), 0, 2*x(3);
               2*x(1), 2*x(2), -4]');
x0 = [1;1;1]; tol= 0.00001;  maxit= 10;

xold = x0; iter=1; 
while (iter<= maxit) 
    y= -feval(J,xold)\ feval(fun,xold);
    xnew=xold+y';
    dif = norm(xnew-xold);
    dis([iter   xnew   dif ]);
    if dif <= tol 
        x=xnew ; 
        disp (' Newton method has converged '), return;
    else
        xold= xnew;
    end 
    iter = itr+1;
end 
disp('Newton method did not converge')
x = xnew ;

[Jan]

Using anonymous functions is smarter than the old inline method.

If you get an error message, please be so kind and post a copy of it. It is useful to know, what the error is.

The code fails after a copy&paste already, because the char array inside the inline call is continued over the line breaks.

[Rik]

Another typo in your code:

iter = itr+1;

It looks like this should be

iter = iter+1;

Answer 1

[Jan]

One problem is hidden inside:

fun =inline( '[x(1)^2+ x(2)^2 + x(3)^2 -1 ;
               x(1)^2 + x(3)^2-0.25 ;
               x(1)^2+ x(2)^2 + 4*x(3) ]');

You can omit commas in vectors and unfortunately Matlab interprets [a -1] as 1x2 vector, while [a - 1] is a scalar. So insert spaces around all operators to be clear and unique:

% [EDITED] leading quotes added...
fun = inline('[x(1) ^ 2 + x(2) ^ 2 + x(3) ^ 2 - 1;', ...
              'x(1) ^ 2 + x(3) ^ 2 - 0.25;', ...
              'x(1) ^ 2 + x(2) ^ 2 + 4 * x(3)]');

Note that the editor marks inline as ancient method. Prefer to use an anonymous function instead.

The next problem occurs in

dis([iter   xnew   dif ]);

Do you mean "disp"? The concatenation does not work, because iter is a scalar, but xnew is a column vector.

disp(iter)
disp(xnew)
disp(dif)

[king skiler]

I correct the previous mistakes , but there is another wrong.

[Rik]

As mentioned previously, you should use anonymous functions instead.

Also, if you post something here, post it as text, so we don't have to type everything, but can correct your code here. In this case, Jan made a small typo that is easily correctable:

fun = inline(['[x(1) ^ 2 + x(2) ^ 2 + x(3) ^ 2 - 1;', ...
               'x(1) ^ 2 + x(3) ^ 2 - 0.25;', ...
               'x(1) ^ 2 + x(2) ^ 2 + 4 * x(3)]']);

Moving to an anonymous function is easy from here:

fun = @(x) [x(1) ^ 2 + x(2) ^ 2 + x(3) ^ 2 - 1; ...
            x(1) ^ 2 + x(3) ^ 2 - 0.25; ...
            x(1) ^ 2 + x(2) ^ 2 + 4 * x(3)]);