in structural analysis (3D frame constructions) I compute the system stiffness matrix and do a Cholesky decomposition to get the system displacements. I also need to determin eigenfrequencies of the structure, which is an eigenproblem. For this, it seems, I need to invert the system stiffness matrix and then multiply the mass matrix. So after all, I need to invert... So I guess, I don't need to do the Cholesky decomp, but just invert and use the inversion for the displacements computation. So, poor me, the advantaged of Cholesky are not really useable for me... Or is there a way to use the Cholesky decomposition for the eigenproblem too ?
Background: To give you an idea about the size of the problem at hand: I'm talking about 12 degrees of freedom per element, max 15 elements, exactly 6 degrees of freedom are restrained, max bandwidth 18. So: not really big....
However, it would be nice to solve this issue in a more general, efficient way, so I can use the resulting software for other, larger problems too.
I must use a highly inefficient computer language. FORTRAN, C and Java are no option in my case.