# Existing solver for large scale load dependent Ritz vectors problem

I have a large scale system with the following equations of motions

$M\ddot z(t)+K z(t)=F(t)$

$M$ is the mass matrix

$K$ is the stiffness matrix

And I want to solve the equation for displacement $z(t)$, the eigenvalues and the eigenvectors with load dependent Ritz Analysis ( the algorithm is described succinctly in here).

I know that I can use APRACK to for large scale eigenvalue problems, but what about load dependent Ritz Analysis? Is there already a solver ( commercial, open source, all doesn't matter) out there that does this kind of thing?

Just to be clear, I am looking for a programming library that I can use, not a commercial software that I can't call programmatically .

• Sorry for answering without any prior knowledge on the subject, but to me the algorithm described in your scan looks like it could be implemented very easily using any library that can do the two things: 1) solution of a linear system (in particular, steps (3) and (5)) and 2) matrix-vector products (steps (4), (6) and (7)). This library could be, e.g., SciPy, cholmod, SuperLU, etc. depending on the properties of $K$. – knl Jan 17 '17 at 11:31
• @knl, would you like to post your comment as an answer? Because it is – Graviton Feb 24 '17 at 6:35

The algorithm described in your scan looks like it could be implemented using a library that can do the two things: 1) solution of a linear system (in particular, steps (3) and (5)) and 2) matrix-vector products (steps (4), (6) and (7)). This library could be, e.g., SciPy, cholmod, SuperLU, etc. depending on the properties of the matrix $K$.