I want to solve numericaly (using Matlab) the generalized eigenvalues-eigenvector equation: $(K-w^2M)q=0$.
Where M and K have the following block structures:
$$ M = \begin{bmatrix} M_1 & 0 \\ 0 & 0 \end{bmatrix}$$
$$ K = \begin{bmatrix} K_1 & K_2 \\ K_3 & K_4 \end{bmatrix}$$
I have already resolve it in matlab, but I wanna know if there is a way to save time in this process, because $M$ and $K$ are really big matrices, so I think that I can use the particular form of this matrices to do this.
The problem that I am trying to solve is a band structure, where $w$ is the frequency and $q$ is a displacement of a solid.