Timeline for Compute only selected components of an eigenvector
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2014 at 14:24 | comment | added | gboukensha | Hi Richard. That's very interesting, I'm eager to read your answer! | |
| Oct 28, 2014 at 13:54 | comment | added | Richard Zhang | I deleted my prev answer (it didn't answer your question), but I've actually encountered this exact problem before. One can show that the condition you need on $A$ is that it must be well-approximated by a rank-$O(k)$ reduction. I can write out a full answer when I get time. | |
| Sep 29, 2014 at 15:56 | comment | added | gboukensha | Thanks a lot for your comments. What I'm trying to achieve here is the computation of the heat kernel for a given point of a 2d compact manifold $M$, restricted to the time domain. In particular, given the eigen-decomposition $\Delta_M \phi = \lambda \phi$ of the Laplace-Beltrami operator $\Delta_M$ on $M$, I'm interested in computing the quantity $\sum_{i=1}^m e^{-\lambda_i t} \phi_i(x)^2$ for a given $x\in M$, $t \in \mathbb{R}$ and $m \in \mathbb{N}$. I need to do it very efficiently, that's why I'd like to compute $\phi_i(x)$ instead of the whole $\phi_i$. | |
| Sep 28, 2014 at 17:33 | answer | added | Suvrit | timeline score: 4 | |
| Sep 28, 2014 at 16:01 | comment | added | Suvrit | You may benefit from "random sampling" of $A$... | |
| Sep 28, 2014 at 14:05 | review | Close votes | |||
| Sep 28, 2014 at 17:26 | |||||
| Sep 28, 2014 at 14:01 | comment | added | Federico Poloni | What is your goal here? What are you trying to achieve that doesn't work with the usual large-scale eigenvalue algorithms? | |
| Sep 28, 2014 at 14:01 | history | edited | Ricardo Andrade |
added top-level and quasi-top-level tags
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| Sep 28, 2014 at 13:43 | review | First posts | |||
| Sep 28, 2014 at 14:01 | |||||
| Sep 28, 2014 at 13:43 | history | asked | gboukensha | CC BY-SA 3.0 |