A x = b
This is a frequency dependent problem, where the interested frequency range is 1-300 Hz.
A is a square matrix of 246 by 246, and it consists elements that are dependent on $\omega^2$, and the rest of the elements are either zero or have constant non-zero value. The unknown x is a response vector that is made up by displacement and pressure that have order relation of O(3) ~ O(5) between them depending on the frequency.
For the matrix A, condition number is around $10^7$, with the first 43 eigenvalues are considerably larger than the rest ~O(6).
In this problem, when $\omega$ is larger than 100 Hz, the resonance and anti-resonance frequencies deviates significantly from the FEA-predicted result. I would like to use a regularization technique, which is frequency dependent, to compensate the effect of ill-conditioning.
I have checked the following thread, but I couldn't find a use for the proposed solution where it uses discrete fourier transform.
Regularization of underdetermined system to favour low frequency solutions?
If I were to use Tikhonov regularization, how would I go on to implement a frequency dependent $\Gamma$? Or what would be the computationally efficient alternative ?