How to solve an equation with big matrix?

Hello,

I have a problem solving this type of equation: det((-w^2)*Ma+Ka)==0

I've tried several times, using syms, fsolve, etc... Due to the sizes fo the matrix Ma and Ka that is for both 288X288, the matlab is not able to find the q solutionc of w (that is the unkown), where q is equal to tha arrays of the matrix (288). I've tried this types of code:

1)syms f(x)

f(x) = det(-(x^2)*Ma2+Ka2);

sol = vpasolve(f);

2)syms w

S = det(-(w^2)*Ma+Ka)==0;

solve = S;

3)myfun = @(x)det((-x.^2)*Ma+Ka);

[a,b]=size(Ma);

x0 = zeros(2*a,1);

C = fsolve(@(x)det((-x.^2)*Ma+Ka),x0);

None of them works, any solution? I will appreciate your help.

[Torsten]

What's the size of w in your equation if both Ma and Ka are of size 288x288 ?

Is it a single value (like 5) or a matrix of size 288x288 ?

[Saverio Loiacono]

It’s a column vector with a size equal to the size of the matrix: 288

[Torsten]

And how do you define a column vector of size (288x1) multiplied by a matrix of size (288x288) plus a matrix of size (288x288) ?

E.g.

[2;4;5].^2 * [1 2 3;4 5 6;7 8 9] + [10 11 12;13 14 15;16 17 18] 

Error using *
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To operate on each element of the matrix individually, use TIMES (.*) for elementwise multiplication.

?

[Saverio Loiacono]

I’m sorry w ,that is the unknown,is a number, it is not a vector. And from the equation I should obtain 288 solution for w. That is for clarity a frequency.

[Saverio Loiacono]

So it’s a single value as you defined it before

Answer 1

[Torsten]

Looks like a generalized eigenvalue problem of the form

(A - w^2*B)*x = 0

with unknown x and w.

Use "eig" to solve it.

[Saverio Loiacono]

Ok, but eig of what? C = (-w^2)*Ma+Ka D= eig(C) Like this?

[Torsten]

From the documentation:

[V,D,W] = eig(A,B)

The generalized eigenvalue problem is to determine the solution to the equation Av = λBv, where A and B are n-by-n matrices, v is a column vector of length n, and λ is a scalar. The values of λ that satisfy the equation are the generalized eigenvalues. The corresponding values of v are the generalized right eigenvectors. The left eigenvectors, w, satisfy the equation w’A = λw’B.

Thus in your case:

e = eig(Ka,Ma)

The elements of e are your elements w^2. Taking the positive and negative square roots give you the 2*288 possible values for w.

[Saverio Loiacono]

thank you so much, I appreciate your help.