How to solve an equation with big matrix?
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Saverio Loiacono
am 2 Feb. 2024
Kommentiert: Saverio Loiacono
am 2 Feb. 2024
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.
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Torsten
am 2 Feb. 2024
Bearbeitet: Torsten
am 2 Feb. 2024
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.
3 Kommentare
Torsten
am 2 Feb. 2024
Bearbeitet: Torsten
am 2 Feb. 2024
From the documentation:
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.
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