All Questions

Let $H = \triangle + V(x) : \mathbb{R}^2 \rightarrow \mathbb{R}^2$. I am interested in domain decomposition for an eigenproblem involving $H$. The lowest 1000 eigenfunctions of $H$, $ \psi_i $, can ...

I am wondering whether it is possible to compute portions of the eigenvectors of a given (possibly very big) matrix. More formally, consider the eigenvalue problem $\mathbf{Ax} = \lambda \mathbf{x}$, ...

I'm trying to find the eigenvector corresponding to the second smallest eigenvalue of a large $(4,000,000 \times 4,000,000)$ matrix $L$. $L$ is a graph Laplacian, with the following structure: $L = D -...

Consider a matrix $A\in\mathbb{R}^{n\times n}$ and a projector $P\in\mathbb{R}^{n\times n}$. Are there results regarding the generalized eigenpairs $(v,\lambda)$ of the generalized eigenproblem $$...

Consider the following problem that is known to be non-convex but can be solved as a generalized eigenvalue problem (i.e. has a global optimum solution): $\underset{w}{\text{maximize}}\quad w^{\top}...