1

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 ?

Community
  • 1
ivanfield
  • 11
  • Just 246x246 then even dense matrices (one big DFT matrix without any factorization into FFT matrices) should be OK. A term like ${\bf C|Dv|}_2$ where D is DFT matrix, C is diagonal weight matrix, larger weights for the vector components corresponding to noisy / unwanted frequencies. – mathreadler Mar 29 '17 at 08:15
  • $\bf v$ is the time domain vector you regularize on / minimize with respect to. – mathreadler Mar 29 '17 at 08:21

0 Answers0