Finding Eigenvalues from an equation

Hello,

Im looking to find eigenvalues from an equation. Cosh(wx)*cos(wx)+1=0. For this equation i am looking for four different values dealing with w=1,2,3,4. Having trouble getting these in matlab? Any ideas?

[Roger Stafford]

If you tell us what you mean by "eigenvalues from an equation", perhaps we can help. Normally, eigenvalues are associated with a set of linear equations, but your equations are not linear in x.

Answer 1

[Star Strider]

I’m not sure what you’re trying, but if you’re looking for four different values of x corresponding to the different values of w, this works:

        for w = 1:4
            eqn = @(x) cosh(w.*x) .* cos(w.*x) + 1;
            xval(w) = fzero(eqn, 1);
        end

This gives:

xval = 1.8751e+000   937.5520e-003   625.0347e-003     1.1735e+000

[Mike]

I got it to work, but its only gives the correct value for the first computation. If i change fzero(eqn , 1) from 1 to 4, 7, and 10 then i get all the correct answers. And idea how i can get all those to compute at once?

[Star Strider]

I’m not sure what you mean by ‘all the correct answers’. There are several roots for each value of w, and the roots fzero finds depend on the starting point. Which ones are the ‘correct’ roots?

This will work:

        for w = 1:4
            eqn = @(x) cosh(w.*x) .* cos(w.*x) + 1;
            [xval, fval] = fzero(eqn, 1);
            vmat(w,:) = [w  xval  fval];
        end

with

vmat =

       1.0000e+000     1.8751e+000   222.0446e-018
       2.0000e+000   937.5520e-003   222.0446e-018
       3.0000e+000   625.0347e-003  -666.1338e-018
       4.0000e+000     1.1735e+000   -23.9808e-015

The code is correct, and produces the correct answers. The rv matrix the following code produces is identical to vmat. The only difference is that eqn2 takes w as a specific argument. (The fzero function takes only one-parameter functions, and uses whatever is in the workspace for the other values in the function, so I couldn’t use eqn2 with it.)

        eqn2 = @(w,x) cosh(w.*x) .* cos(w.*x) + 1;
        for k1 = 1:4
            fnv = eqn2(vmat(k1,1), vmat(k1,2));
            rv(k1,:) = [vmat(k1,1), vmat(k1,2), fnv];
        end

I feel vindicated.