3 ms·
Interesting. That isn't excessively large for distributed-memory Krylov-subspace eigensolvers (e.g., SLEPc). Do you have a good reference for the current algori
by poulson 13y ago
Interesting. That isn't excessively large for distributed-memory Krylov-subspace eigensolvers (e.g., SLEPc). Do you have a good reference for the current algorithms used? And how large is the nullspace typically?
EDIT: I assume this [1] is what you're referring to, which draws from the following algorithms of Coppersmith [2,3].
[1]: http://eprint.iacr.org/2010/006.pdf http://eprint.iacr.org/2010/006.pdf
[2]: https://www.sciencedirect.com/science/article/pii/002437959390235G?np=y https://www.sciencedirect.com/science/article/pii/0024379593...
[3]: http://thales.doa.fmph.uniba.sk/macaj/skola/seminar/CoppersmithMOC62.pdf http://thales.doa.fmph.uniba.sk/macaj/skola/seminar/Coppersm...
- pbsd 13y agoYes, that is correct. Generally the block Lanczos variant used in practice is Montgomery's [1], though, not Coppersmith's. Lanczos was popular until a few years ago, as it requires slightly less actual matrix-vector multiplications, but since Wiedemann can be partially distributed it is becoming more desirable. [1] http://link.springer.com/content/pdf/10.1007%2F3-540-49264-X_9.pdf http://link.springer.com/content/pdf/10.1007%2F3-540-49264-X...