Timeline for Operator compression preserving lowest energy eigenspace.
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 6, 2011 at 21:35 | comment | added | dranxo | Yes, you only need to form $Av$ to do Lanczos. My matrix is exactly this $\mathbb{H}$: en.wikipedia.org/wiki/Configuration_interaction . I would like it to be smaller while still preserving the lowest energy states. A similar problem arises in finite element simulations. Consider coarsening the discretization in certain regions in order to work with a smaller stiffness matrix. Normally this is done using geometric intuition but in my problem the space is high dimensional so I would like to somehow automate the coarsening. | |
| May 6, 2011 at 7:03 | comment | added | Federico Poloni | You do not need to form the matrix to run Lanczos, you just need a "black-box" function that computes $Av$ given a vector $v$. If you cannot even do this efficiently, please specify how you can interact with the matrix, or which special structure it has. | |
| May 6, 2011 at 4:39 | comment | added | dranxo | Sorta, but that's not what I want here. I am trying to compress the operator without first computing an invariant subspace. It would be great if one could identify which entries of the matrix contribute most to the eigenvectors without explicitly forming the matrix (it's about 90GB in RAM). If you think this sounds crazy that makes two of us. Ideally my advisor would be the third but no luck there. | |
| May 5, 2011 at 21:14 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |